UN Representation Research Articles

The cycle index of the automorphism group of Zn

We consider the group action of the automorphism group Un = Aut(Zn) on the set Zn, that is the set of residue classes modulo n. Clearly, this group action provides a representation of Un as a permutation group acting on n points. One problem to be solved regarding this group action is to find its cycle index. Once it is found, there appears a vast class of related enumerative and computational problems with interesting applications. We provide the cycle index of specified group action in two ways. One of them is more abstract and hence compact, while another one is basically a procedure of composing the cycle index from some building blocks. However, those building blocks are also well explained and finally presented in a very detailed fashion.

Outer Mongolia and the Changing Dynamics of UN Representation: Impacts on U.S. China Policy, 1961

In 1961, the Kennedy administration confronted wides-pread domestic and foreign anticipation that significant changes would be made to existing U.S. China policy. Although the new administration proposed to liberate the United States from past policies and offer fresh, innova-tive solutions to problems confronted worldwide, the major issues that characterized and defined the American relationship with both the Chinese Communists on the mainland and the Chinese Nationalists on Taiwan posed a challenge for the new President and his top advisers. This study examines the Kennedy administration’s deli-berations at the United Nations with regard to the Outer Mongolian representation matter and mounting interna-tional pressures from U.S. allies and other nations for the United States to assume a more flexible posture toward Communist China. Despite the lack of a major departure from existing policies, initiatives proposing a reappraisal of U.S. China policy during the Kennedy administration precipitated discussions and debates that contributed sig-nificantly to the eventual transformation of Sino-Ameri-can relations.

Outer Mongolia and the Changing Dynamics of UN Representation: Impacts on U.S. China Policy, 1961

Outer Mongolia and the Changing Dynamics of UN Representation: Impacts on U.S. China Policy, 1961

The Costs of Realism: The Nixon Administration, the People’s Republic of China, and the United Nations

The Nixon presidency has been pivotal in debates on American Cold War foreign policy and domestic politics. Recent access to primary sources now allows more precise analyses of the relationship between the Nixon administration and the United Nations in general and the problem of Chinese UN representation in particular. The representation question conditioned the actions of the UN starting from the 1950s and was in turn influenced by the new policy adopted by Richard Nixon and Henry Kissinger toward the People’s Republic of China in 1971. Until now, analysis of White House strategy toward the PRC concentrated on the period preceding Peking’s admission to the United Nations or considered the admission question only marginally. This essay focuses on PRC admission to the United Nations, setting it within the context of the opening of dialog between the United States and China and of the realist strategy adopted by the White House, underlining the differences between the positions of the White House and of the Department of State.

Chinese UN Representation at the Crossroads: International Pressures for Change in U.S. China Policy, 1961

In 1961, the Kennedy administration confronted widespread domestic and foreign anticipation that significant changes would be made to existing U.S. China policy. Although the new administration proposed to liberate the United States from past policies and offer fresh, innovative solutions to problems confronted worldwide, the major issues that characterized and defined the American relationship with both the Chinese Communists on the mainland and the Chinese Nationalists on Taiwan posed a challenge for the new President and his top advisers. This study examines the Kennedy administration’s deliberations with regard to the Chinese representation matter at the United Nations and mounting international pressures from U.S. allies and other nations for the United States to assume a more flexible posture toward Communist China. Despite the lack of a major departure from existing policies, initiatives proposing a reappraisal of U.S. China policy during the Kennedy administration precipitated discussions and debates that significantly contributed to the evolution towards the eventual transformation of Sino-American relations.

Chinese UN Representation at the Crossroads: International Pressures for Change in U.S. China Policy, 1961

Chinese UN Representation at the Crossroads: International Pressures for Change in U.S. China Policy, 1961

The Weil Character of the Unitary Group Associated to a Finite Local Ring

AbstractLetR/R be a quadratic extension of finite, commutative, local and principal rings of odd characteristic. Denote byUn(R) the unitary group of ranknassociated toR/R. The Weil representation ofUn(R) is defined and its character is explicitly computed.

The UN activities of the International Union of Psychological Science in 2001

The major thrust of the IUPsyS activities at the UN this year has been the establishment, in early 2001, of a permanent team of New York area psychologists willing to voluntarily represent the Union at the different meetings held throughout the year at the UN Secretariat in New York under the auspices of the UN Department of Public Information, the Economic and Social Council (ECOSOC), as well as some of the other UN agencies also active in New York, such as UNICEF and UNESCO. With the help of the International Affairs Office of the American Psychological Association, which we would like to thank, we had access to the names of New York area psychologists who were interested in doing UN representation for psychology. Four of them were identified as prime candidates and were interviewed. Their nomination as UN/NGO representatives was approved by the Executive Committee of the Union. I am very happy to inform our national members and affiliate organizations that Dr. Fritz Galette, Dr. Margarita Garcia‐Estevez, Dr. Douglas Y Seiden and Ms. Carolee E. Iltis have generously accepted to act as the Union's NGO representatives in New York. The decision to appoint four representatives was determined by the workload associated with the activities of the UN Secretariat (e.g., Dept of Public Information ‐NGO Briefings every week, multiple meetings of numerous committees dealing with mental health, health, ageing, children, human rights, women issues), plus numerous Preparatory Committees for General Assembly Summits (presently, three upcoming summits on racism, children and women that we will briefly discuss later in this report). Therefore, we felt it was important to be realistic and to appoint several individuals who are ready to share the work to be done and provide 1–2 days per month of their time.

UN Representation Disputes: A Case Study of Cambodia and a New Accreditation Proposal for the Twenty-First Century

UN Representation Disputes: A Case Study of Cambodia and a New Accreditation Proposal for the Twenty-First Century

The reduced Gassner representation restricted to a normal free subgroup of the pure braid group

We show that the reduced Gassner representation restricted to a normal free subgroup U n of the pure braid group, P n , is essentially the Magnus representation of U n / U '' n provided that the indeterminate y, used in defining this representation, is set to be one. Then, as a corollary, Lipschutz's result follows easily that is, in general, the kernel of the reduced Gassner representation restricted to U n is a subgroup of U '' n .

The Gel’fand–Tsetlin representations of the unitary Cayley–Klein algebras

The explicit expressions of the operators of the irreducible representations of the unitary Cayley–Klein algebras un(j) are obtained from the well-known Gel’fand–Tsetlin representations of un . The contractions of the representations of u2(j1) and u3(j1,j2) are regarded as examples. This approach gives the representations of the contracted algebras in different bases, for example, in discrete and continuous ones. Possible contractions of the irreducible representations are discussed.

On theU N group integral with variables in the adjoint representation and the twisted chiral model

We consider the generalized one-link group integral for group variables and external sources in the adjoint representation ofUN. We develop the strong and weak couplings of this class of integral. Special attention is paid to the case of a source matrix proportional to the identity, which we treat by a saddle point method. The case of twisted chiral models is reconsidered, including the effects of nontrivial maxima. They are argued not to affect the large-N limit of the model and to exist also in the standard lattice chiral model.

Condition that All Irreducible Representations of a Compact Lie Group, if Restricted to a Subgroup, Contain no Representation More than Once

One of the results of the theory of the irreducible representations of the unitary group in n dimensions Un is that these representations, if restricted to the subgroup Un-1 leaving a vector (let us say the unit vector e1 along the first coordinate axis) invariant, do not contain any irreducible representation of this Un-1 more than once (see [1, Chapter X and Equation (10.21)]; the irreducible representations of the unitary group were first determined by I. Schur in his doctoral dissertation (Berlin, 1901)). Some time ago, a criterion for this situation was derived for finite groups [3] and the purpose of the present article is to prove the aforementioned result for compact Lie groups, and to apply it to the theory of the representations of Un.

Algebraic identities for parafermi statistics of given order

It is pointed out that the structure of parafermion algebras generated byN pairs of creation and annihilation operators is determined by the unique occurrence of certain representations ofUN in particular representations ofSO2N andSO2N+1, identified by the eigenvalues of their invariants. This observation is used to derive a variety of identities satisfied by the creation and annihilation operators, which are characteristic of the orderp of the parastatistics. The «statistical quantum number» of Ohnuki and Kamefuchi is identified with the invariant ofSO2N and related in turn to the invariants ofUN. A simple method is stated for the systematic determination of special identities, some of which are already known.

Group Theory of Harmonic Oscillators in n-Dimensional Space

It is shown how the states of N particles which move in a common n-dimensional harmonic oscillator potential can be classified according to the irreducible representations of the unitary groups UN or Un. The complete set of Nn independent integrals of the motion is obtained, their simultaneous eigenvectors being generalized Gel'fand basis vectors which can be enumerated either as bases for irreducible representations of UN or Un. Explicit formulas are given for the linear transformations induced on the basis vectors by the infinitesimal operators of UN and Un. The relation of the present work for n = 3 to that of Bargmann and Moshinsky is noted.