Quantum K-theory Chevalley formulas in the parabolic case.

We derive cancellation-free Chevalley-type multiplication formulas for the T -equivariant quantum K -theory ring 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 ring of arbitrary flag manifolds G / B , which was derived earlier in terms of the quantum alcove model, by the last three authors. [ABSTRACT FROM AUTHOR]