A representation of su q (n) , which diverges in the limit of q → 1, is investigated. This is an infinite dimensional and a non-unitary representation , defined for the real value of q, 0 < q < 1. Each irreducible representation is specified by n continuous variables and one discrete variable. This representation gives a new solution of the Yang-Baxter equation, when the R-matrix is evaluated. ...

We give the first two-dimensional pictorial presentation of Berele’s correspondence [B], an analogue of the Robinson-Schensted (R-S) correspondence [Ri, Se] for the symplectic group Sp(2n,C). From the standpoint of representation theory, the R-S correspondence combinatorially describes the irreducible decomposition of the tensor powers of the natural representation of GL(n,C). Berele’s insertio...

A classical theorem of Stone and von Neumann says that the Schrödinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of square-integrable functions on configuration space. Using the Wigner-Moyal transform we construct an irreducible representation of the Heisenberg group on a certain Hilbert space of square-integr...

We classify all massive irreducible representations of super Poincaré in D = 10. New Casimir operators of super Poincaré are presented whose eigenvalues completely specify the representation. It is shown that a scalar superfield contains three irreducible representations of massive supersymmetry and we find the corresponding superprojectors. We apply these new tools to the quantization of the m...

Our goal is to describe factorizations of the characters of irreducible representations of compact semisimple Lie groups. It is well-known that for a given Lie group G of rank n, the Virtual Representation Ring R(G) with the operations of tensor product, direct sum, and direct difference is isomorphic to a polynomial ring with integer coefficients and number of generators equal to n. As such, R...

A basic problem in the representation theory of a compact Lie group is to calculate the restriction of an irreducible representation of K to a closed subgroup. Most classical results on this problem concern connected groups. We’ll recall some of those, and talk about some of the modifications needed to work with disconnected groups. 1. Weight multiplicities Suppose g is a complex semisimple Lie...

In its most general formulation a quantum kinematical system is described by a Heisenberg group; the ”configuration space” in this case corresponds to a maximal isotropic subgroup. We study irreducible models for Heisenberg groups based on compact maximal isotropic subgroups. It is shown that if the Heisenberg group is 2-regular, but the subgroup is not, the ”vacuum sector” of the irreducible r...

By embedding a Toeplitz matrix-vector product (MVP) of dimension n into a circulant MVP of dimension N = 2n+ δ− 1, where δ can be any nonnegative integer, we present a GF(2) multiplication algorithm. This algorithm leads to a new redundant representation, and it has two merits: 1. The flexible choices of δ make it possible to select a proper N such that the multiplication operation in ring GF(2...

Let G2(q) be the finite Chevalley group of type G2 defined over a finite field with q = p elements, where p is a prime number and n is a positive integer. In this paper, we determine when the restriction of an absolutely irreducible representation of G in characteristics other than p to a maximal subgroup of G2(q) is still irreducible. Similar results are obtained for B2(q) and G2(q).