R matrix for generalized quantum group of type A

2020/01/13 by Jae-Hoon Kwon, Kwon, JaeHoon, Jeongwoo Yu +1 · 1 citation
Mathematics · #17B10 #17B37 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2001.04119

openalex publication_date 2020/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The generalized quantum group U(ε) of type A is an affine analogue of quantum group associated to a general linear Lie superalgebra \mathfrakgl_M|N. We prove that there exists a unique R matrix on tensor product of fundamental type representations of U(ε) for arbitrary parameter sequence ε corresponding to a non-conjugate Borel subalgebra of \mathfrakgl_M|N. We give an explicit description of its spectral decomposition, and then as an application, construct a family of finite-dimensional irreducible U(ε)-modules which have subspaces isomorphic to the Kirillov-Reshetikhin modules of usual affine type A_M-1⁽¹⁾ or A_N-1⁽¹⁾.

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