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.

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)