A Chevalley formula for the equivariant quantum $K$-theory of cominuscule varieties

By Anders Skovsted Buch, P. Chaput, Leonardo Constantin Mihalcea, N. Perrin. Algebraic Geometry, 2016

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We prove a type-uniform Chevalley formula for multiplication with divisor classes in the equivariant quantum $K$-theory ring of any cominuscule flag variety $G/P$. We also prove that multiplication with divisor classes determines the equivariant quantum $K$-theory of arbitrary flag varieties. These results prove a conjecture of Gorbounov and Korff concerning the equivariant quantum $K$-theory of Grassmannians of Lie type A.

Subfields: Geometry and Topology, Mathematical Physics

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