A conjectural Peterson isomorphism in K-theory

被引：11

作者：

Lam, Thomas ^{[1
]}

Li, Changzheng ^{[2
]}

Mihalcea, Leonardo C. ^{[3
]}

Shimozono, Mark ^{[3
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Guangdong, Peoples R China

[3] Virginia Tech, Dept Math, 460 McBryde Hall, Blacksburg, VA 24061 USA

来源：

JOURNAL OF ALGEBRA | 2018年 / 513卷

关键词：

Flag manifolds; Affine Grassmannian; Quantum K theory; Khomology of the affine; Grassmannian; QUANTUM COHOMOLOGY; FLAG MANIFOLDS; VARIETIES; FINITENESS;

D O I：

10.1016/j.jalgebra.2018.07.029

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We state a precise conjectural isomorphism between localizations of the equivariant quantum K-theory ring of a flag variety and the equivariant K-homology ring of the affine Grassmannian, in particular relating their Schubert bases and structure constants. This generalizes Peterson's isomorphism in (co)homology. We prove a formula for the Pontryagin structure constants in the K-homology ring, and we use it to check our conjecture in few situations. Published by Elsevier Inc.

引用

页码：326 / 343

页数：18

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[2]

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