Quantum K-theory Chevalley formulas in the parabolic case

2021/09/23 by Takafumi Kouno, Cristian Lenart, Kouno, Takafumi +7 · 2 citations
Mathematics · #05E10 #14M15 #14N15 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2109.11596

openalex publication_date 2021/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive cancellation-free Chevalley-type multiplication formulas in the T-equivariant quantum K-theory of Grassmannians of type A and C, and also those of two-step flag manifolds of type A. They are obtained based on the uniform Chevalley formula in the T-equivariant quantum K-theory of arbitrary flag manifolds G/B, which was derived earlier in terms of the quantum alcove model, by the last three authors.

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• Conjectural Positivity for Pontryagin Product in Equivariant K-theory of Loop Groups
• Towards small quantum Chern character

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