Character Formulas for Kirillov-Reshetikhin Modules via Folding of Supercharacters of \mathfrakgl(M|N)

2025/12/09 by Tsuboi, Zengo
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2512.08791

openalex publication_date 2025/12/09 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28

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 \mathfrakgl(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).

Citations

• Quantum correspondences of affine Lie superalgebras
• Representations of quantum affine algebras of type B_N
• Crystal Bases for the Quantum Superalgebra U_q(gl(m,n))
• Tensor product representations for orthosymplectic Lie superalgebras
• Twisting of quantum (super)algebras. Connection of Drinfeld's and Cartan-Weyl realizations for quantum affine algebras

Related

• On the theory of q-characters for quantum affine superalgebras of type A
• Finite Dimensional Representations of Quantum Affine Algebras
• Quantum Character Theory
• Representations of affine superalgebras and mock theta functions
• Kirillov-Reshetikhin modules of generalized quantum group of type A