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

Abstract

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.

version 2: 28 pages; few examples, and a simplified Chevalley formula in the minuscule case, are added

References in corpus (4)

• Quantum Integrability and Generalised Quantum Schubert Calculus
• Equivariant K-theory of Grassmannians
• Puzzles, positroid varieties, and equivariant K-theory of Grassmannians
• Projected Gromov-Witten varieties in cominuscule spaces

Cited by in corpus (5)

• Quantum Integrability and Generalised Quantum Schubert Calculus
• Towards Landau-Ginzburg models for cominuscule spaces via the exceptional cominuscule family
• A conjectural Peterson isomorphism in K-theory
• Euler characteristics of cominuscule quantum K-theory
• Positivity determines the quantum cohomology of Grassmannians