Representations Of Group Research Articles

The Baker-Coon-Romans N-point amplitude and an exact field theory limit of the Coon amplitude

We study the N-point Coon amplitude discovered first by Baker and Coon in the 1970s and then again independently by Romans in the 1980s. This Baker-Coon-Romans (BCR) amplitude retains several properties of tree-level string amplitudes, namely duality and factorization, with a q-deformed version of the string spectrum. Although the formula for the N-point BCR amplitude is only valid for q > 1, the four-point case admits a straightforward extension to all q ≥ 0 which reproduces the usual expression for the four-point Coon amplitude. At five points, there are inconsistencies with factorization when pushing q < 1. Despite these issues, we find a new relation between the five-point BCR amplitude and Cheung and Remmen’s four-point basic hypergeometric amplitude, placing the latter within the broader family of Coon amplitudes. Finally, we compute the q → ∞ limit of the N-point BCR amplitudes and discover an exact correspondence between these amplitudes and the field theory amplitudes of a scalar transforming in the adjoint representation of a global symmetry group with an infinite set of non-derivative single-trace interaction terms. This correspondence at q = ∞ is the first definitive realization of the Coon amplitude (in any limit) from a field theory described by an explicit Lagrangian.

Compatible pants decomposition for $\mathrm{SL}_{2}(\mathbb{C})$ representations of surface groups

For any irreducible representation of a surface group into \mathrm{SL}_{2}(\mathbb{C}) , we show that there exists a pants decomposition where the restriction to any pair of pants is irreducible and where no curve of the decomposition is sent to a trace \pm 2 element. We prove a similar property for \mathrm{SO}_{3} -representations. We also investigate the type of pants decomposition that can occur in this setting for a given representation. This result was announced by Detcherry and Santharoubane (2022), motivated by the study of the Azumaya locus of the skein algebra of surfaces at roots of unity.

Realizing regular representations of finite groups

Given a regular representation of a finite group G and a positive integer number n, we construct a (finite) topological space X such that its group of homotopy classes of self-homotopy equivalences E(X) and its group of homeomorphisms Aut(X) are isomorphic to G, and the action of G on the n-th homology group Hn(X) is the regular representation. We also discuss other representations.

Putting People First: A Multimodal Bi‐Stream Structure‐based Model for Bias Mitigation

ABSTRACTResearch into multimodal model biases has largely concentrated on gender and racial issues, neglecting key areas such as biases related to religion, nationality, sexual orientation, and disabilities, as well as the subtleties of question intent and common biases. To address these gaps, we developed the Multimodal Bi‐Stream Structure‐based Model (MBSS) for Bias Mitigation, an innovative approach that focuses on these underrepresented groups by focusing on religion, nationality, sexual orientation, and disability but also to identify common biases and question intents. The MBSS employs a dual stream bias mitigation system, where the standard stream addresses common biases and the mitigation stream targets specific biases, allowing for nuanced and effective bias reduction by making decisions based on the difference in predicted probabilities between these two streams. Empirical results demonstrate MBSS's efficacy, especially in reducing religious bias by up to 71%, highlighting its potential to foster a more inclusive digital environment and enhance the representation of diverse groups.

A note on the Loewy lengths of baby Verma modules for modular Lie algebras

Let G be a connected reductive algebraic group over an algebraically closed field k of prime characteristic p, and g=Lie(G). We study the representations of the reductive Lie algebra g with p-character χ of standard Levi-form in this note. We obtain the similar results about the translation functor and the wall-crossing functor of simple modules parallelling to the representations of algebraic groups (cf. [16, II.Lem.7.20]). Moreover, we get the Loewy lengths of baby Verma modules provided the Vogan Conjecture holds.

CFT Correlators and Mapping Class Group Averages

Mapping class group averages appear in the study of 3D gravity partition functions. In this paper, we work with 3D topological field theories to establish a bulk-boundary correspondence between such averages and correlators of 2D rational CFTs whose chiral mapping class group representations are irreducible and satisfy a finiteness property. We show that Ising-type modular fusion categories satisfy these properties on surfaces with or without field insertions, extending results in [1], and we comment on the absence of invertible global symmetries in the examples we consider.

Racial and ethnic representation of youth in type 1 diabetes interventional trials

BackgroundUnderrepresentation of racial and ethnic groups in clinical trials can limit generalizability of research findings and equitable access to treatment. This study evaluates racial and ethnic representation of youth in US-based interventional trials on childhood type 1 diabetes (T1D). MethodsThis cross-sectional study examined interventional trials of T1D conducted in the US and registered on ClinicalTrials.gov. Trials were included if completed as of June 6, 2023, began between years 2010 and 2022, and exclusively enrolled youth ≤19 years old. We assessed representation of racial and ethnic groups in T1D trials, estimated using the enrollment-prevalence difference (EPD). ResultsA total of 106 trials were eligible for inclusion. Of those eligible, 62 (58 %) trials reported participant race or ethnicity and were included in the analyses. Significant disparities in enrollment were observed for American Indian/Alaska Native, Asian/Pacific Islander, Black, and Hispanic youth compared to their respective contribution to disease burden among youth in the US. Disparities in trial enrollment were greatest for Black (EPD, −10.2; 95 % confidence interval [CI], −14.4 to −7.9) and Hispanic (EPD, −7.7; 95 % CI, −12.6 to −4.8) youth. EPDs of trials conducted prior to year 2017 did not differ significantly from those conducted as of year 2017. ConclusionsHistorically marginalized racial and ethnic youth were underrepresented in T1D trials. Strategies to improve recruitment of these populations are needed to reduce inequities in diabetes treatment and outcomes.

Beyond victimhood and perpetration: Reconstruction of the ingroup's historical role in eight Eastern and Western European countries under Nazi occupation

AbstractThe Nazi regime's aggressive expansion across Europe during WWII created a landscape of suffering, resistance, and collaboration. How do lay Europeans today reconstruct their ingroup's roles during Nazi occupation, and how do different role representations relate to defensive responses aimed at protecting the ingroup from threat? We tested two theoretical predictions: Following the identity threat prediction, we expected that denying culpability but endorsing morally favorable group representations (e.g., victim‐heroism) would represent an ingroup‐defensive strategy, correlating with other defensive responses, such as victim‐directed negativity or victim‐blaming. Following the identity management prediction, we expected that precisely accepting culpability and acknowledging threatening representations (e.g., willing collaboration with Germans) would form the basis for a defensive stance and thus correlate with defensive intergroup reactions. Analyzing data from nine European samples spanning eight countries (N = 5474), we found support for the identity management prediction in six contexts: Lay representations as willing collaborators were associated with negative collective emotions and correlated with victim‐directed negativity, whereas victim‐hero representations showed no such connections. The remaining three countries revealed a mixture of the two identity accounts. We discuss implications for understanding historical representations and identity protection in groups that were both victims and perpetrators of massive intergroup atrocities.

Linkage and translation for tensor products of representations of simple algebraic groups and quantum groups

AbstractLet be either a simple linear algebraic group over an algebraically closed field of characteristic or a quantum group at an ‐th root of unity. We define a tensor ideal of singular ‐modules in the category of finite‐dimensional ‐modules and study the associated quotient category , called the regular quotient. For , the Coxeter number of , we establish a ‘linkage principle’ and a ‘translation principle’ for tensor products: Let be the essential image in of the principal block of . We first show that is closed under tensor products in . Then we prove that the monoidal structure of is governed to a large extent by the monoidal structure of . These results can be combined to give an external tensor product decomposition , where denotes the Verlinde category of .

Symmetry Shapes Thermodynamics of Macroscopic Quantum Systems.

We derive a systematic approach to the thermodynamics of quantum systems based on the underlying symmetry groups. We first show that the entropy of a system can be described in terms of group-theoretical quantities that are largely independent of the details of its density matrix. We then apply our technique to generic N identical interacting d-level quantum systems. Using permutation invariance, we find that, for large N, the entropy displays a universal asymptotic behavior in terms of a function s(x) that is completely independent of the microscopic details of the model, but depends only on the size of the irreducible representations of the permutation group S_{N}. In turn, the equilibrium state of the system and macroscopic fluctuations around it are shown to satisfy a large deviation principle with a rate function f(x)=e(x)-β^{-1}s(x), where e(x) only depends on the ground state energy of particular subspaces determined by group representation theory, and β is the inverse temperature. We apply our theory to the transverse-field Curie-Weiss model, a minimal model of phase transition exhibiting an interplay of thermal and quantum fluctuations.

Unveiling Disparities: Analyzing Hispanic Inclusion in Liver Cancer Research Databases in the United States

AbstractPrimary liver cancer, including hepatocellular carcinoma and intrahepatic cholangiocarcinoma was the sixth leading cause of cancer death in the United States in 2023. Hispanic people constitute approximately 19% of the nation’s total population according to the US Census. Hispanic patients have the highest relative incidence rates of liver cancer compared to non-Hispanic Whites and non-Hispanic Blacks, a disparity frequently overlooked in cancer research. In this study, our primary objective was to analyze the potential underrepresentation of Hispanic individuals in liver cancer research databases. We identified databases that had liver cancer-specific studies and be population-based in the United States. Our search yielded 7 cancer genomic databases, which were analyzed according to incidence percentages across ethnicity and race categories. Our study included 3104 patients; ethnic data was not reported for 13.1% (n = 406) of the patients. Samples were predominantly from individuals who identified as Not Hispanic (81.0%), Hispanic individuals represented 5.9%. Race was reported as follows: non-Hispanic Whites (61.0%), Asians (22.0%), non-Hispanic Blacks (5.4%), Other (3.1%), Native American/American Indian/Alaska Native (0.4%), Pacific Islander/Native Hawaiian (0.2%) and not reported (7.9%). These findings collectively underscore significant disparities in the representation of ethnic and racial groups, particularly Hispanics. Given the present racial and ethnic demographics of the US population and the projected surge in the Hispanic population in forthcoming years, it becomes imperative to address health disparities that may worsen without efforts to enhance proper inclusion in cancer research.

Wave front sets of nilpotent Lie group representations

Let G be a nilpotent, connected, simply connected Lie group with Lie algebra g, and π a unitary representation of G. In this article we prove that the wave front set of π coincides with the asymptotic cone of the orbital support of π, i.e. WF(π)=AC(⋃σ∈supp(π)Oσ), where Oσ⊂ig⁎ is the coadjoint Kirillov orbit associated to the irreducible unitary representation σ∈Gˆ.

Characteristics of inpatient and outpatient respiratory syncytial virus mortality in Gavi-eligible countries

The current understanding of the RSV-related mortality age distribution in low- and lower-middle-income countries (LMICs) relies on a limited number of disease incidence studies reporting wide age bands, and lacking specificity to Gavi-eligible countries. Understanding the age distribution of RSV-related deaths is crucial for the implementation of RSV interventions in LMICs that rely on support from Gavi. This study aims to provide the age profile of RSV mortality specifically in Gavi-eligible countries.Utilizing data from the RSV GOLD project, an ongoing global online mortality registry focusing on children under the age of 5 with laboratory-confirmed RSV infection, we employed two models (Complete Data Model and Prospective Data Model) to estimate the age profiles. To mitigate biases related to age group representation, we applied post-stratification weighting in our analysis.We included 423 pediatric deaths, including 145 from the community, under 2 years of age from 15 Gavi-eligible countries. Both models identified a peak age at 1 month and found that the majority of RSV-related mortality cases (59–77 %) from Gavi-eligible countries occur before 6 months of life. However, the models exhibited disparities in other age-related metrics. We present fitted age-at-time-of-death probability distributions to aid impact and cost-effectiveness studies.We expect that implementing infant RSV immunization strategies, such as maternal vaccination or infant immunoprophylaxis, will have high impact on RSV-related mortality in Gavi-eligible countries. The divergent results from the two models underscore the importance of carefully considering potential biases in retrospective and surveillance data when interpreting the age profile of RSV mortality cases in future research.

‘Can women have it all?’ Transitions in media representations of Jacinda Ardern’s leadership and identity by a global newsroom

ABSTRACT The paper examines changing media representations of Jacinda Ardern, former Aotearoa New Zealand Prime Minister, from the global broadcaster, BBC News Online, across three key milestones in the politician’s career: her appointment, re-election and resignation. Our socio-semantic analysis of this representation demonstrates how the media intersect her professional identity with age, gender, social class, and later, her identity as a mother. Whilst earlier coverage of Ardern’s career praises her successfully reconciling these aspects of her personal, social and professional identities, later coverage implies that ‘having it all’ was never really possible longer term. We argue that the visibility of this discourse, and the focus on intersectional aspects of Ardern’s personal and social identities, leads to her resignation being positively evaluated as her ‘finally’ succumbing and committing to the ‘natural’ inevitabilities of heterosexual family life. The article considers what such representation means for Ardern and women politicians and leaders more broadly, and contextualises these findings in relation to existing research on media representations of women in politics and leadership. Finally, we also consider the value of a more longitudinal approach to tracking the cumulative effects of the representation of social actors and groups.

A - 5 Longitudinal Analysis of Protective Factors on Cognition Following Total Knee Arthroplasty

Abstract Objective To examine cognitive and brain resilience factors on older adult cognition following total knee arthroplasty (TKA). Methods Participants were recruited through orthopedic clinics and screened for eligibility (i.e., age &amp;gt; 60 years, English as first language, diagnosis of knee osteoarthritis, intact activities of daily living). Data were collected before surgery, three weeks, three months, and one-year post-TKA (N = 67; mean(SD) age = 69.49(7.09) years; mean(SD) education = 15.62(2.83) years; 51% female; 90% non-Hispanic White (NHW), 10% non-Hispanic Black. Participants received baseline magnetic resonance imaging (3 T Siemens Verio). Magnetization-prepared rapid gradient-echo images were preprocessed. Machine learning predicted brain age (DeepBrainNet) was calculated for each participant. Linear mixed effects models examined longitudinal effects of word reading (Wide Range Achievement Test-III (WRAT-III)), brain age gap (predicted brain age minus chronological age), sex, ethnicity/race, pain interference (Brief Pain Inventory), and depression (Beck Depression Inventory-II) on cognitive composites (i.e., memory, working memory/inhibition, reasoning, processing speed, language). Results Memory, working memory/inhibition, reasoning, and processing speed had curvilinear trajectories (p’s &amp;lt; 0.05), declining post-TKA and subsequently returning to baseline. Word reading positively associated with memory (β = 0.065, SE = 0.016, p &amp;lt; 0.001), working memory/inhibition (β = 0.069, SE = 0.016, p &amp;lt; 0.001), reasoning (β = 0.099, SE = 0.021, p &amp;lt; 0.001), and processing speed (β = 0.050, SE = 0.015, p &amp;lt; 0.01). Language negatively associated with BAG (β = −0.041, SE = 0.017, p &amp;lt; 0.05). Women had higher processing speed (β = −0.285, SE = 0.135, p &amp;lt; 0.05), and NHW participants had higher memory (β = 0.479, SE = 0.224, p &amp;lt; 0.05). When pain interference was higher, processing speed (β = −0.003, SE = 0.002, p &amp;lt; 0.05) and language (β = −0.007, SE = 0.002, p &amp;lt; 0.01) were lower. Conclusions Cognitive and brain resilience measures may identify individuals protected against cognitive dysfunction post-surgically. Future research increasing representation in underrepresented groups is warranted.

The Impact of the 2020 BLM Resurgence on the Racial Representations of Ads and Ad Evaluations: Analysis of Super Bowl Ads

Using ads from four Super Bowl broadcasts (2019–2022), we examined the impacts of the 2020 Black Lives Matter (BLM) resurgence on the ad representations of diverse racial groups and the evaluations of ads featuring Black models. Findings show increases in quantitative representations (number and duration) for Black ad models, but this improvement was not linked to qualitative representations (portrayal, prominent role, and hierarchy status). Findings also show the limited influence of the 2020 BLM resurgence on evaluations of advertisements featuring Black models. We also examined how the impact of the 2020 BLM resurgence on advertising shifted from 2021 to 2022.

Commutative avatars of representations of semisimple Lie groups

Here we announce the construction and properties of a big commutative subalgebra of the Kirillov algebra attached to a finite dimensional irreducible representation of a complex semisimple Lie group. They are commutative finite flat algebras over the cohomology of the classifying space of the group. They are isomorphic with the equivariant intersection cohomology of affine Schubert varieties, endowing the latter with a new ring structure. Study of the finer aspects of the structure of the big algebras will also furnish the stalks of the intersection cohomology with ring structure, thus ringifying Lusztig's q-weight multiplicity polynomials i.e., certain affine Kazhdan-Lusztig polynomials.

Lattice dynamics of Bi12GeO20 crystal: Polarized Raman scattering and first-principles analysis

Our paper presents a combined experimental and theoretical study of the lattice dynamics of Bi12GeO20 crystal. Polarized Raman spectra were measured in two x-ray oriented single crystals. In a crystal of cubic symmetry, phonon modes of A- and E-types are spectroscopically indistinguishable. Using a special experimental technique, we separated the phonon modes that transform according to A and E irreducible representations. Since the number of E-type lines observed in Raman scattering is higher than theoretically allowed by group theory, we performed a first-principles calculation of the Bi12GeO20 lattice dynamics to accurately identify the symmetry of phonon modes. All experimental lines observed in Raman scattering are classified according to irreducible representations of the cubic I23 group. Using samples of different thicknesses, 10 mm and 0.120 mm, we have demonstrated that the optical activity plays an insignificant role at Raman backscattering in Bi12GeO20 crystal.

Existence of elementwise invariant vectors in representations of symmetric groups

Existence of elementwise invariant vectors in representations of symmetric groups

Sowing green seeds of mind: exploring the determinants of green mindfulness among university students

Purpose This study aims to investigate the determinants influencing green mindfulness among university students in Malaysia within the context of the Malaysia 2030 Agenda, focusing on Sustainable Development Goal 17 attainment. Design/methodology/approach The research uses a quantitative approach with a sample of 203 young adults. It explores the factors of goal difficulty, knowledge and awareness, spirituality, values and perceived university environmental responsibility (PUER), using a novel theoretical framework termed universal identity theory (IT). Findings Values, knowledge and awareness and PUER significantly contribute to green mindfulness, whereas spirituality and goal difficulty did not exhibit a substantial relationship to green mindfulness. Research limitations/implications Limited representation of diverse age groups and the potential influence of seniority on spirituality. Future research should expand the framework to include green behavior and performance, increase the sample size and consider a broader age demographic. Practical implications Universities play a crucial role in promoting green mindfulness through the establishment of rules, regulations, environmental initiatives, incentive systems and the introduction of a green mindfulness course. Clear communication channels and top-down approaches are recommended. Social implications This research contributes to understanding the mechanisms that induce green mindfulness among university students in Malaysia, aligning with national and global sustainability goals. Originality/value The universal IT provides a comprehensive understanding of how personal, social and community-based identities collectively influence green mindfulness. This theoretical perspective contributes to the environmental psychology and sustainability studies field, offering a culturally sensitive approach.