Symplectic tableaux and quantum symmetric pairs

2023/08/03 by Watanabe, Hideya · 2 citations
#05E10 #17B10 #17B37 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2308.01718

Abstract

We provide a new branching rule from the general linear group GL_2n(ℂ) to the symplectic group Sp_2n(ℂ) by establishing a simple algorithm which gives rise to a bijection from the set of semistandard tableaux of a fixed shape to a disjoint union of several copies of sets of symplectic tableaux of various shapes. The algorithm arises from representation theory of a quantum symmetric pair of type AII_2n-1, which is a q-analogue of the classical symmetric pair (\mathfrakgl_2n(ℂ), \mathfraksp_2n(ℂ)).

Cited by

• Berele row-insertion and quantum symmetric pairs
• Symplectic Branching through Crystals

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