Canonical bases via pairing monomials

2023/08/30 by Jonas Antor, Antor, Jonas · 1 citation
Mathematics · #17B37 (Primary) 20C08 #20G05 (Secondary) #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.2308.16254

openalex publication_date 2023/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any quantum group of finite ADE type, we prove a new formula for the standard bilinear form evaluated at monomials. Combining this with ideas from the Lusztig-Shoji algorithm, we obtain a new algorithm that computes the canonical basis. In type A, the algorithm also computes composition multiplicities of standard modules for the affine Hecke algebra of GL_n and we explain how the algorithm can be extended to compute the dimensions of simple modules.

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• Canonical bases in Lie theory and total positivity

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