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

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

doi:10.14231/AG-2018-015

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

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

Rutgers University–New Brunswick
Nancy Université
Virginia Polytechnic Institute and State University
Laboratoire de Mathématiques de Versailles

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Pages (from-to)	568-595
Number of pages	28
Journal	Algebraic Geometry
Volume	5
Issue number	5
DOIs	https://doi.org/10.14231/AG-2018-015
Publication status	Published - 1 Sept 2018
Externally published	Yes

Keywords

Chevalley formula
Comi- nuscule ag varieties
Gromov-Witten invariants
Molev-Sagan equations
Quantum K-theory
Schubert structure constants

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10.14231/AG-2018-015

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

keywords = "Chevalley formula, Comi- nuscule ag varieties, Gromov-Witten invariants, Molev-Sagan equations, Quantum K-theory, Schubert structure constants",

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AU - Buch, Anders S.

AU - Chaput, Pierre Emmanuel

AU - Mihalcea, Leonardo C.

AU - Perrin, Nicolas

N1 - Publisher Copyright: © Foundation Compositio Mathematica 2018.

PY - 2018/9/1

Y1 - 2018/9/1

N2 - We prove a type-uniform Chevalley formula for multiplication with divisor classes in the equivariant quantum K-theory ring of any cominuscule ag variety G=P. We also prove that multiplication with divisor classes determines the equivariant quantum K- theory of arbitrary ag varieties. These results prove a conjecture of Gorbounov and Korff concerning the equivariant quantum K-theory of Grassmannians of Lie type A.

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

KW - Chevalley formula

KW - Comi- nuscule ag varieties

KW - Gromov-Witten invariants

KW - Molev-Sagan equations

KW - Quantum K-theory

KW - Schubert structure constants

UR - https://www.scopus.com/pages/publications/85052563987

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DO - 10.14231/AG-2018-015

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VL - 5

SP - 568

EP - 595

JO - Algebraic Geometry

JF - Algebraic Geometry

IS - 5

ER -

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

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Keywords

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