A unified and complete construction of all finite dimensional irreducible representations of gl(2|2)

Representations of the non-semisimple superalgebra gl(2/2) in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of gl(2/2) are constructed explicity through the explicit construction of all gl(2) circle plus gl(2) particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of gl(2/2) in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.

Useful representations of series solutions for transport problems

Simple techniques are presented for rearrangement of an infinite series in a systematic way such that the convergence of the resulting expression is accelerated. These procedures also allow calculation of required boundary derivatives. Several examples of conduction and diffusion-reaction problems illustrate the methods.

Level-one highest weight representations of U-q[g1(1 vertical bar 1)] and associated vertex operators

We study the level-one irreducible highest weight representations of U-q[gl(1\1)] and associated q-vertex operators. We obtain the exchange relations satisfied by these vertex operators. The characters and supercharacters associated with these irreducible representations are calculated'. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (0(m)vertical bar alpha(n)) representations of U-q[gl(m vertical bar n)]

We detail the automatic construction of R matrices corresponding to (the tensor products of) the (O-m\alpha(n)) families of highest-weight representations of the quantum superalgebras Uq[gl(m\n)]. These representations are irreducible, contain a free complex parameter a, and are 2(mn)-dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a total of 2(4mn) components, each of which is in general an algebraic expression in the two complex variables q and a. Although the constructions are straightforward, we describe them in full here, to fill a perceived gap in the literature. As the algorithms are generally impracticable for manual calculation, we have implemented the entire process in MATHEMATICA; illustrating our results with U-q [gl(3\1)]. (C) 2002 Published by Elsevier Science B.V.

Link invariants associated with gauge equivalent solutions of the Yang-Baxter equation: The one-parameter family of minimal typical representations of Uq[gl(2|1)]

In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that it is possible to obtain invariants of regular isotopy (as defined by Kauffman) which may not be ambient isotopic. We illustrate our results with explicit computations using solutions of the trigonometric Yang-Baxter equation associated with the one-parameter family of minimal typical representations of the quantum superalgebra U-q,[gl(2/1)]. We have implemented MATHEMATICA code to evaluate the invariants for all prime knots up to 10 crossings.

Wishing for political dominance: Representations of history and community in 'Queer Theory'

Suggests that one's sense of one's self and one's sexuality may also have a close relationship to non-fiction texts about gay and lesbian cultures. Reliance of people's sense of being gay on literary representations; Popularity and authority of the book "Queer Theory," by Annamarie Jagose; Disagreements that characterize lesbian and gay historiography in Australia.

Coherent state construction of representations of osp(2|2) and primary fields of osp(2|2) conformal field theory

Representations of the superalgebra osp(2/2)(k)((1)) and current superalgebra. osp(2/2)k in the standard basis are investigated. All finite-dimensional typical and atypical representations of osp(2/2) are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with osp(2/2)(k)((1)) in the standard basis are obtained for arbitrary level k. (C) 2004 Elsevier B.V. All rights reserved.

Determinant representations of correlation functions for the supersymmetric t-J model

Working in the F-basis provided by the factorizing F-matrix, the scalar products of Bethe states for the supersymmetric t-J model are represented by determinants. By means of these results, we obtain determinant representations of correlation functions for the model.