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

2000/01/31 by Wen-Li Yang, Wen‐Li Yang, Yao-Zhong Zhang
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Affine transformation #Algebra over a field #Algebraic structures and combinatorial models #Bosonization #Combinatorics #Fermion #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Superalgebra #Vertex (graph theory) #math-ph #math.MP #math.QA

paper · pdf · doi:10.1063/1.533441

published as J. Math. Phys. 41 (2000) 5849-5869 · LaTex file 21 pages

arxiv created 2000/02/24 · openalex publication_date 2000/08/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• N-point correlation functions of the spin-1 XXZ model
• Algebraic Bethe ansatz for gl(2, 1) invariant 36-vertex models