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

被引：18

作者：

Buch, Anders S. ^{[1
]}

Chaput, Pierre-Emmanuel ^{[2
]}

Mihalcea, Leonardo C. ^{[3
]}

Perrin, Nicolas ^{[4
]}

机构：

[1] Rutgers State Univ, Dept Math, 110 Frelinghuysen Rd, Piscataway, NJ 08854 USA

[2] Univ Lorraine, Domaine Sci Victor Grignard, 239 Blvd Aiguillettes,BP 70239, F-54506 Vandoeuvre Les Nancy, France

[3] Virginia Tech Univ, Dept Math, 460 McBryde, Blacksburg, VA 24060 USA

[4] Univ Paris Saclay, CNRS, UVSQ, Lab Math Versailles, F-78035 Versailles, France

来源：

ALGEBRAIC GEOMETRY | 2018年 / 5卷 / 05期

关键词：

quantum k-theory; Chevalley formula; Gromov-Witten invariants; Schubert structure constants; cominuscule flag varieties; Molev-Sagan equations; COHOMOLOGY; POSITIVITY; PUZZLES; RING;

D O I：

10.14231/AG-2018-015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：568 / 595

页数：28

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