Type E7 Research Articles

The Rost invariant has trivial kernel for quasi-split groups of low rank

For G a simple simply connected algebraic group defined over a field F, Rost has shown that there exists a canonical map R_G : H^1(F, G) \rightarrow H^3(F, \mathbb{Q} / \mathbb{Z}(2)) . This includes the Arason invariant for quadratic forms and Rost's mod 3 invariant for exceptional Jordan algebras as special cases. We show that RG has trivial kernel if G is quasi-split of type E6 or E7. A case-by-case analysis shows that it has trivial kernel whenever G is quasi-split of low rank.

THE AUTOMORPHISMS GROUP OF THE MULTIPLICATIVE CARTAN DECOMPOSITION OF LIE ALGEBRA E8

We construct a new basis for the exceptional simple Lie algebra L of type E8 and describe the multiplication rule in this basis. It allows to find the action of generators of automorphism group of the multiplicative Cartan decomposition of L on this basis.

B-Functions of the Prehomogeneous Vector Space Arising from a Cuspidal Character Sheaf of E7

The purpose of this paper is to compute the explicit form of the relative invariants and their b-functions of a certain important prehomogeneous vector space appearing in the study of a cuspidal character sheaf of the exceptional group E7. For every simple algebraic group excepting the type E7, the b-functions of this kind of prehomogeneous vector space have been determined.

Structurable Algebras and Groups of Type E6 and E7

It is well known that every group of type F4 is the automorphism group of an exceptional Jordan algebra, and that up to isogeny all groups of type 1E6 with trivial Tits algebras arise as the isometry groups of norm forms of such Jordan algebras. We describe a similar relationship between groups of type E6 and groups of type E7 and use it to give explicit descriptions of the homogeneous projective varieties associated to groups of type E7 with trivial Tits algebras.

Embeddings ofPSL(2, 41) andPSL(2, 49) inE8(C)

We classify embeddings of the finite simple groups PSL(2, 41) andPSL (2, 49) into algebraic groups of type E8in characteristic not dividing the orders of these respective groups. Lie theory and finite group theory point to families of elements in a group of typeE8 over a finite field which might satisfy a presentation for our finite simple group. Techniques from computational representation theory identify all suitable systems of generators. We describe a number of methods of computation in Chevalley groups of type E8.

Sequence variants and functional analysis of human papillomavirus type 16 E5 gene in clinical specimens.

Previously, we found that the E5 protein can be expressed in HPV-16 infected precancerous lesions and cervical cancer. In this study, we investigated the presence of sequence variants of E5 in HPV-16 infected tissues. Toward this end, we amplified the E5 gene by polymerase chain reaction from 29 HPV-16 infected tissues including eight normal tissues, seven high grade neoplastic tissues (high grade squamous intraepithelial lesions (HSIL) and 14 cervical cancer tissues. Sequence analysis demonstrated that there were three mutational hot spots at positions 3979, 4042, and 4077 of the HPV-16 DNA; these and other mutations resulted in six variants in the E5 sequence. This resulted in four E5 protein mutants, named WTE5 [wild type E5 protein], 14E5, 21E5 and 56E5. Functional analysis of these four mutant proteins revealed that the transforming activities of 14E5, 21E5 and 56E5 were 0.95, 0.59, and 0.89 fold of WTE5, respectively. Although E5 was expressed in all of the HSIL and cervical cancer tissues, but in only one of the eight normal tissues tested, only WT E5 protein was found in HSIL while in cervical cancer tissues both WT and mutant E5 proteins were detected. Since these E5 proteins exhibited the same in vitro transforming activity, these data suggest that expression of E5 is important in development and progression toward malignancy but mutation of E5 does not affect the transformation process.

Left Cells in the Weyl Group of Type E8

The aim of the present paper is to give an explicit description for all the left cells of the Weyl group W of type E8. We first find a representative set Σ for the left cells of W and then use it to describe these cells. Our results show that most of the left cells in W can be characterized by their generalized τ-invariants alone. Then the remaining ones (which are called exceptional left cells) are characterized by the generalized τ-invariants together with the a-values.

Generating cytotoxic t lymphocytes against cervical carcinoma with lentivirus transduced antigen presenting cells

Human Papillomavirus (HPV), the cause of cervical cancer, infects and immortalizes keratinocytes. Since the infected cells present viral antigens but lack co-stimulatory molecules for inducing immune responses, alternative antigen presenting cells (APCs) are needed. The 98aa HPV-E7 oncoprotein represents an attractive immunotherapy target, as it is overexpressed and vital for immortalization. Recent publications report abrogated transforming ability and destabilization of E7 following C58G and C91G mutations in ‘CXXC’ zinc finger motifs at positions 58–61 and 91–94. We have made 7 mutant E7 proteins including C94V mutation. This disrupts the zinc finger motifs, but preserves the T cell receptor region of the immunogenic 86–94 nonamer and increases its HLA-0201 binding 14-fold, based on anchor position affinities. The expression and stability of the wild type and mutant E7 (m-E7) proteins is being determined in transfected homozygous HLA-A0201 Epstein-Barr Virus transformed B-cells (LCLs). The mutant with peak E7 peptide processing and presentation will be determined using a HLA-A0201 specific T-cell clone recognizing E711–20. Based on transduction efficiencies of GFP with various gene transfer methods, we have designed a T-cell stimulation scheme in which m-E7 transduced autologous dendritic cells (DCs) and LCLs are used as priming and restimulating APCs, respectively. Using VSV-G pseudotyped recombinant human lent-virus, we detected >40% transduction efficiency in CD34+ derived DCs and >60% in LCLs. We believe that m-E7 specific cytotoxic T lymphocytes can be generated ex vivo with lentivirus modified patient-derived DCs and LCLs and that these CTLs will provide a potent treatment for cervical carcinoma.

Borwein Identity and Vertex Operator Algebras

We will prove the Borwein identity by computing the characters of some automorphisms of the lattice vertex operator algebra (VOA) of type E6. As similar examples, we will prove two identities containing the famous Jacobi identity, which was also obtained from the VOA of type D4 by Frenkel–Lepowsky–Meurman. Our method is a variant of observations made by the above authors.

Allosteric Activation of Acid α-Glucosidase by the Human Papillomavirus E7 Protein

Changes in the cellular carbohydrate metabolism are a hallmark of malignant transformation and represent one of the earliest discernible events in tumorigenesis. In the early stages of certain epithelial cancers, a metabolic switch is regularly observed, in which slowly growing glycogenotic cells are converted to highly proliferating basophilic cells. This step is accompanied by a rapid depletion of the intracellular glycogen stores, which in liver carcinogenesis results from the activation of the enzyme acid alpha-glucosidase by an as yet unknown mechanism. We show here that acid alpha-glucosidase is a target for the E7 protein encoded by human papillomavirus type 16, a human tumor virus that plays a key role in the genesis of cervical carcinoma. We show that expression of E7 induces the catalytic activity of acid alpha-glucosidase in vivo and wild type E7, but not transformation-deficient mutants bind directly to acid alpha-glucosidase and increase the catalytic activity of the enzyme in vitro. The data suggest that the E7 protein encoded by human papillomavirus type 16 can act as an allosteric activator of acid alpha-glucosidase.

HPV16 E6 oncogene variants in women with cervical intraepithelial neoplasia

Human papillomaviruses (HPVs) are strongly associated with the development of high grade cervical intraepithelial neoplasia (CIN) and cervical carcinoma, with between 40-80% of patients with cervical carcinoma being attributed to a single HPV type, HPV16 depending on the methods used and geographical location of the particular study [van den Brule et al., 1996]. An HPV16 E6 variant has been described which is strongly associated with high grade CIN [Ellis et al., 1997] and with the human leukocyte antigen (HLA)-B7 genotype in women with cervical carcinoma where HLA-B7 positive patients were demonstrated to have a significantly poorer clinical outcome [Ellis et al., 1995]. To determine whether this HPV16 E6 variant might play a significant role in the pathogenesis of cervical disease, 174 HPV16 positive women were selected from those attending the colposcopy clinics of Guy's and St Thomas' Hospital Trust following polymerase chain reaction (PCR) amplification of HPV16 L1 or E5 DNAs from cervical brush swabs or fixed biopsy tissue. HPV16 E6 DNA was amplified by PCR and the variant sequence was identified by Msp 1 restriction enzyme digestion, as the nucleotide substitution creates an additional unique Msp 1 site. The study group comprised 29 normal controls, 7 women with borderline cytology, 123 women with cervical dysplasia and 12 women with cervical cancer. 101/174 (58%) of these women had amplifiable E6 DNA and restriction enzyme digestion was performed on 95 of these. The variant E6 sequence was identified in 3/95 (3%) individuals, two of whom had normal histology and one had a CIN II lesion. Wild type E6 sequence was identified in the remaining 92/95 (97%) individuals. These data suggest that this particular E6 variant does not play a major role in the pathogenesis of HPV16 related cervical disease in women living in the South London area. J. Med. Virol. 60:337–341, 2000. © 2000 Wiley-Liss, Inc.

Axisymmetric, Three-Integral Models of Galaxies: A Massive Black Hole in NGC 3379

We fit axisymmetric three-integral dynamical models to NGC 3379 using the line-of-sight velocity distribution obtained from Hubble Space Telescope FOS spectra of the galaxy center and ground-based long-slit spectroscopy along four position angles, with the light distribution constrained by WFPC2 and ground-based images. We have fitted models with inclinations from 29° (intrinsic galaxy type E5) to 90° (intrinsic E1) and black hole masses from 0 to 109 M⊙. The best-fit black hole masses range from 6 × 107 to 2 × 108 M⊙, depending on inclination. The preferred inclination is 90° (edge-on); however, the constraints on allowed inclination are not very strong, owing to our assumption of constant M/LV. The velocity ellipsoid of the best model is not consistent with either isotropy or a two-integral distribution function. Along the major axis, the velocity ellipsoid becomes tangential at the innermost bin, radial in the midrange radii, and tangential again at the outermost bins. The rotation rises quickly at small radii owing to the presence of the black hole. For the acceptable models, the radial-to-tangential [(σ + σ)/2] dispersion in the midrange radii ranges over 1.1 < σr/σt < 1.7, with the smaller black holes requiring larger radial anisotropy. Compared with these three-integral models, two-integral isotropic models overestimate the black hole mass since they cannot provide adequate radial motion. However, the models presented in this paper still contain restrictive assumptions—namely, assumptions of constant M/LV and spheroidal symmetry—requiring yet more models to study black hole properties in complete generality.

HPV16 E6 oncogene variants in women with cervical intraepithelial neoplasia

Human papillomaviruses (HPVs) are strongly associated with the development of high grade cervical intraepithelial neoplasia (CIN) and cervical carcinoma, with between 40-80% of patients with cervical carcinoma being attributed to a single HPV type, HPV16 depending on the methods used and geographical location of the particular study [van den Brule et al., 1996]. An HPV16 E6 variant has been described which is strongly associated with high grade CIN [Ellis et al., 1997] and with the human leukocyte antigen (HLA)-B7 genotype in women with cervical carcinoma where HLA-B7 positive patients were demonstrated to have a significantly poorer clinical outcome [Ellis et al., 1995]. To determine whether this HPV16 E6 variant might play a significant role in the pathogenesis of cervical disease, 174 HPV16 positive women were selected from those attending the colposcopy clinics of Guy's and St Thomas' Hospital Trust following polymerase chain reaction (PCR) amplification of HPV16 L1 or E5 DNAs from cervical brush swabs or fixed biopsy tissue. HPV16 E6 DNA was amplified by PCR and the variant sequence was identified by Msp 1 restriction enzyme digestion, as the nucleotide substitution creates an additional unique Msp 1 site. The study group comprised 29 normal controls, 7 women with borderline cytology, 123 women with cervical dysplasia and 12 women with cervical cancer. 101/174 (58%) of these women had amplifiable E6 DNA and restriction enzyme digestion was performed on 95 of these. The variant E6 sequence was identified in 3/95 (3%) individuals, two of whom had normal histology and one had a CIN II lesion. Wild type E6 sequence was identified in the remaining 92/95 (97%) individuals. These data suggest that this particular E6 variant does not play a major role in the pathogenesis of HPV16 related cervical disease in women living in the South London area.

Expression of Human Papilloma Virus E7 Protein Causes Apoptosis and Inhibits DNA Synthesis in Primary Hepatocytes via Increased Expression of p21Cip-1/WAF1/MDA6

The impact of human papilloma virus (HPV16) E7 proteins and retinoblastoma (RB) antisense oligonucleotides upon mitogen-activated protein kinase (MAPK)-mediated inhibition of DNA synthesis via p21(Cip-1/WAF1/MDA6) (p21) was determined in primary hepatocytes. Prolonged activation of the MAPK pathway in p21(+/+) or p21(-/-) hepatocytes caused a large decrease and increase, respectively, in DNA synthesis. Either transfection with RB antisense oligonucleotides, expression of wild type E7, or RB binding mutant E7 (C24S) proteins increased p21 levels and reduced DNA synthesis in p21(+/+) hepatocytes. RB antisense oligonucleotides and E7 proteins increased apoptosis in p21(+/+), but not p21(-/-), hepatocytes. Expression of wild type E7 increased DNA synthesis above control levels in p21(-/-) cells, which was additive with prolonged MAPK activation. In contrast, expression of mutant E7 did not alter DNA synthesis above control levels in p21(-/-) cells and was supra-additive with prolonged MAPK activation. Antisense ablation of RB in p21(-/-) hepatocytes had a weak stimulatory effect upon DNA synthesis itself but enhanced the capacity of mutant E7 protein to stimulate DNA synthesis to the same level observed using wild type E7. The ability of prolonged MAPK activation to stimulate DNA synthesis in the presence of mutant E7 and antisense RB was additive. Collectively, the present data demonstrate that loss of RB function together with loss of p21 function plays an important role in the E7- and MAPK-dependent modulation of apoptosis and DNA synthesis in primary hepatocytes.

The distinguished involutions of the weyl group of type E 6

In [1] Kazhdan and Lusztig defined the concepts of left. right. and two-sided cells for the Coxeter group (W,S) which play an important role in the representation theory of its associated Hecke algebra. The concept of left cell has its origin in the work of Robinson and Shensted, who described a 1-1 correspondence between the synlmetric group S n and the set of pairs of standard Yong tableallx of the sanle shape, of size n. In this picture, a left cell of S n. appears as the subset of S n corresponding to the set of pairs with fixed. In 1982, Barbasch and Vogan clescribe explicitly the left cells of the Weyl group of the type B n, D n by using prin1itive ideals in the envelopillg algebra of a con1plex sen1isin1ple Lie algebra. In [8] Tong (jIlangqing describes explicitly the left cells of the Weyl group of the type E6 by using the method introduced by Shiin [6]. Lusztig shows that each 1eft cell of W contains a unique distinguished involution which play an imporatant role in the ring J given in G. Lllsztig [3]. In this paper vve find all distinguished involutions for the Weyl group of type E6. The paper is organized as follows. In Section 1 we recall some general results on the relation the a-function, and distinguished involutions for Weyl groups. In Section:2 we describe canonical expressions for elernents of the Weyl group of type E6. In Section 3 we describe explicitly a11 distinguished involutions for the Weyl group W of type E6.

Simple singularities and topology of symplectically filling 4-manifold

Topological restrictions of symplectically filling 4-manifolds of links around simple singularities are studied by using the Seiberg-Witten monopole equations. In particular, the intersection form of minimal symplectically filling 4-manifolds of the singularity of type E 8 is determined. Moreover, for the case of simply elliptic singularities, similar restrictions are obtained. In the proof, a vanishing theorem of the Seiberg-Witten invariant is discussed.

Configurations of seven lines on the real projective plane and the root system of type E7

Let l1,l2,...,l7 be mutually different seven lines on the real projective plane. We consider two conditions;(A) No three of l1,l2,...,l7 intersect at a point. (B) There is no conic tangent to any six of l1,l2, . . . , l7. Cummings [3] and White [16] showed that there are eleven non-equivalent classes of systems of seven lines with condition (A)(cf. [7], Chap. 18). The purposes of this article is to give an interpretation of the classification of Cummings and White in terms of the root system of type E7. To accomplish this, it is better to add condition (B) for systems of seven lines. Moreover we need the notion of tetrahedral sets which consist of ten roots modulo slgns in the root system of type E7 and which plays an important role in our study.

Steinberg modules and Donkin pairs

First we prove that in characteristicp>0 a module with good filtration for a group of type E6 restricts to a module with good filtration for a group of type F4. Thus we confirm a conjecture of Brundan for one more case. Our method relies on the canonical Frobenius splittings of Mathieu. Next we settle the remaining cases, with a computer-aided variation on the old method of Donkin.

A Class of Supercuspidal Representations of G2(k)

AbstractLet H be an exceptional, adjoint group of type E6 and split rank 2, over a p-adic field k. In this article we discuss the restriction of the minimal representation of H to a dual pair PD× × G2(k), where D is a division algebra of dimension 9 over k. In particular, we discover an interesting class of supercuspidal representations of G2(k).

HS &lt;E 7 (5)

In this paper we describe our discovery that the sporadic simple groups HS and M22 are contained in the simple Chevalley group E7(5). The work of [9] produces a short list of the possibilities for a sporadic simple subgroup of an exceptional group of Lie type. Apart from possible embeddings of M22 and HS in groups of type E7 in characteristic 5, all of the embeddings of [9] are already known to occur. Thus our paper completes the classification of sporadic simple subgroups of exceptional groups of Lie type. We give two proofs of the embedding HS<E7(5). The first of these proofs is entirely computer free, while the second proof makes some use of machine calculations. As a step in our hand proof of HS<E7(5) we establish the embedding M22<E7(5): of course, since M22 is a subgroup of HS, this result also follows as a consequence of our computer proof of HS<E7(5). We were led to conjecture the inclusion HS<E7(5) for the following reasons (similar arguments are presented in [9]). The double cover 2.HS has a faithful 56-dimensional character, whose values are compatible with the character values of groups of type E7 acting on their natural 56-dimensional module. Now HS and 2.HS contain a subgroup 52:20, an elementary abelian group of order 25 extended by a cyclic group of order 20 acting faithfully on the 52. Since 20 is not the order of an element in the Weyl group W(E7) = 2×S6(2), it can be shown that 52:20 does not embed in groups of type E7(K), where K is a field of characteristic prime to 5. Thus HS embeds in E7(q) only if 5∣q. On the other hand, all local subgroups of 2.HS embed in 2.E7(5), where our conjecture HS<E7(5). Throughout, G denotes the double cover 2.E7(5), Ḡ denotes the simple group E7(5), and V denotes the natural 56-dimensional module for G over GF(5). Most of our notation follows that of the atlas [4]. The two sections of our paper are completely independent.