Quantum K-theory Chevalley formulas in the parabolic case
Takafumi Kouno, Cristian Lenart, Satoshi Naito, and Daisuke Sagaki,, with an Appendix by Takafumi Kouno, Cristian Lenart, Satoshi Naito, Daisuke, Sagaki, and Weihong Xu
TL;DR
This paper develops explicit multiplication formulas in the T-equivariant quantum K-theory of certain flag varieties, extending previous uniform Chevalley formulas to specific Grassmannians and flag manifolds.
Contribution
It provides cancellation-free Chevalley-type formulas for quantum K-theory in the parabolic case, based on a general formula for arbitrary flag manifolds.
Findings
Formulas for Grassmannians of type A and C
Formulas for two-step flag manifolds of type A
Extension of the quantum alcove model approach
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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra