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arXiv:math/0001154 · Journal of Mathematical Physics

Level-one highest weight representation of Uq[sl(N|1)] and Bosonization of the multicomponent Super t−J model

Wen‐Li Yang, Yao-Zhong Zhang

Published Aug 1, 2000• 6 citations
arXivHTMLPDF

Abstract

We study the level-one irreducible highest weight representations of the quantum affine superalgebra Uq[sl(N̂|1)], and calculate their characters and supercharacters. We obtain bosonized q-vertex operators acting on the irreducible Uq[sl(N̂|1)] modules and derive the exchange relations satisfied by the vertex operators. We give the bosonization of the multicomponent super t−J model by using the bosonized vertex operators.

DOI
10.1063/1.533441

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In this paper, we present a detailed analysis of the diagonalization of the higher spin Heisenberg model using its quantum affine symmetry Uq(sl(2)^)U_q(\hat{sl(2)})Uq​(sl(2)^​). In particular, we describe the bosonizations of the latter algebra, its highest weight representations, vertex operators and screening operators. Finally, we use this bosonization method to compute the vacuum-to-vacuum expectation values and the form factors of any local operator.
In this paper we continue the study of Q-operators in the six-vertex model and its higher spin generalizations. In [1] we derived a new expression for the higher spin R-matrix associated with the affine quantum algebra Uq(sl(2)ˆ). Taking a special limit in this R-matrix we obtained new formulas for the Q-operators acting in the tensor product of representation spaces with arbitrary complex spin. Here we use a different strategy and construct Q-operators as integral operators with factorized kernels based on the original Baxter's method used in the solution of the eight-vertex model. We compare this approach with the method developed in [1] and find the explicit connection between two constructions. We also discuss a reduction to the case of finite-dimensional representations with (half-)integer spins.
Extending the method proposed in [1], we derive QQ-relations (functional relations among Baxter Q-functions) and T-functions (eigenvalues of transfer matrices) for fusion vertex models associated with the twisted quantum affine superalgebras Uq(gl(2r+1|2s)(2)), Uq(gl(2r|2s+1)(2)), Uq(gl(2r|2s)(2)), Uq(osp(2r|2s)(2)) and the untwisted quantum affine orthosymplectic superalgebras Uq(osp(2r+1|2s)(1)) and Uq(osp(2r|2s)(1)) (and their Yangian counterparts, Y(osp(2r+1|2s)) and Y(osp(2r|2s))) as reductions (a kind of folding) of those associated with Uq(gl(M|N)(1)). In particular, we reproduce previously proposed generating functions (difference operators) of the T-functions for the symmetric or anti-symmetric representations, and tableau sum expressions for more general representations for orthosymplectic superalgebras [2], [3], and obtain Wronskian-type expressions (analogues of Weyl-type character formulas) for them. T-functions for spinorial representations are related to reductions of those for asymptotic limits of typical representations of Uq(gl(M|N)(1)).