Based modules over the \imathquantum group of type AI

2021/03/24 by Hideya Watanabe, Watanabe, Hideya · 1 citation
Mathematics · #17B10 #17B37 #Advanced Combinatorial Mathematics #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2103.12932

openalex publication_date 2021/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies classical weight modules over the \imathquantum group U^\imath of type AI. We introduce the notion of based U^\imath-modules by generalizing the notion of based modules over the quantum groups. We prove that each finite-dimensional irreducible classical weight U^\imath-module with integer highest weight is a based U^\imath-module. As a byproduct, a new combinatorial formula for the branching rule from \mathfraksl_n to \mathfrakso_n is obtained.

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