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

Anders S. Buch; Pierre-Emmanuel Chaput; Leonardo C. Mihalcea; Nicolas Perrin

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

Algebraic Geometry 2017-06-12 v2 Combinatorics

Authors: Anders S. Buch , Pierre-Emmanuel Chaput , Leonardo C. Mihalcea , Nicolas Perrin

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.

Keywords

equivariant quantum k-theory chevalley formula cominuscule varieties flag varieties divisor class multiplication grassmannians lie type a

Cite

@article{arxiv.1604.07500,
  title  = {A Chevalley formula for the equivariant quantum K-theory of cominuscule varieties},
  author = {Anders S. Buch and Pierre-Emmanuel Chaput and Leonardo C. Mihalcea and Nicolas Perrin},
  journal= {arXiv preprint arXiv:1604.07500},
  year   = {2017}
}

Comments

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

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

Abstract

Keywords

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