Quantum K-theory Chevalley formulas in the parabolic case
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.
Cite
@article{arxiv.2109.11596,
title = {Quantum K-theory Chevalley formulas in the parabolic case},
author = {Takafumi Kouno and Cristian Lenart and Satoshi Naito and Daisuke Sagaki and with an Appendix by Takafumi Kouno and Cristian Lenart and Satoshi Naito and Daisuke Sagaki and Weihong Xu},
journal= {arXiv preprint arXiv:2109.11596},
year = {2023}
}
Comments
We added the proof of the positivity property for the Chevalley structure constants for full flag manifolds of arbitrary types, two-step flag manifolds of type A, and Grassmannians of type C. We also added Appendix A (a new proof of the existence of a multiplicative surjection due to Kato) and Appendix B (on the connection with a conjecture of Weihong Xu, who is a co-author of this Appendix)