Character Formulas for Kirillov-Reshetikhin Modules via Folding of Supercharacters of $\mathfrak{gl}(M|N)$

Abstract

We derive decomposition formulas for supercharacters of quantum affine ortho-symplectic superalgebras and twisted quantum affine superalgebras into supercharacters of their finite-type quantum sub-superalgebras, by employing Cauchy-type identities for supersymmetric Schur functions. These formulas are obtained via a folding (reduction) procedure applied to the supercharacters of the finite-dimensional general linear Lie superalgebra $\mathfrak{gl}(M|N)$. As a special case, our results provide explicit character formulas for a class of Kirillov--Reshetikhin modules of quantum affine algebras (and their Yangian counterparts), thereby proving a previously proposed conjecture derived from Bethe ansatz analysis (arXiv:2309.16660).

32 pages

References in corpus (9)

• Analytic Bethe Ansatz for Fundamental Representations of Yangians
• Quantum Jacobi-Trudi and Giambelli Formulae for $U_q(B_r^{(1)})$ from Analytic Bethe Ansatz
• Wronskian solutions of the T, Q and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl(M|N)
• Functional Relations and Analytic Bethe Ansatz for Twisted Quantum Affine Algebras
• Analytic Bethe ansatz and functional relations related to tensor-like representations of type II Lie superalgebras B(r|s) and D(r|s)
• Symmetrizable Quantum Affine Superalgebras And Their Representations
• Difference L operators related to q-characters
• Analytic Bethe ansatz related to the Lie superalgebra C(s)
• Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains