A Chevalley formula for the equivariant quantum K-theory of cominuscule   varieties
  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. 
Anders S. Buch, Pierre-Emmanuel Chaput, Leonardo C. Mihalcea and   Nicolas Perrin
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