The Koszul complex and a certain induced module for a quantum group

2022/12/24 by Toshiyuki Tanisaki, Tanisaki, Toshiyuki
Mathematics · #17B37 #20G42 #Advanced Operator Algebra Research #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.2212.12625

openalex publication_date 2022/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a description of a certain induced module for a quantum group of type A. Together with our previous results this gives a proof of Lusztig's conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra of type A_n at the ℓ-th root of unity, where ℓ is an odd integer satisfying (ℓ,n+1)=1 and ℓ> n+1.

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