Quantum Cohomology of Minuscule Homogeneous Spaces III Semi-Simplicity and Consequences

被引：23

作者：

Chaput, P. E. ^{[1
]}

Manivel, L. ^{[2
]}

Perrin, N. ^{[3
]}

机构：

[1] UFR Sci & Tech, Lab Math Jean Leray, Nantes, France

[2] Univ Grenoble 1, Inst Fourier, F-38402 St Martin Dheres, France

[3] Univ Paris 06, Inst Math, Paris, France

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2010年 / 62卷 / 06期

关键词：

quantum cohomology minuscule homogeneous spaces Schubert calculus; quantum Euler class; ORTHOGONAL GRASSMANNIANS; TOTAL POSITIVITY; RINGS;

D O I：

10.4153/CJM-2010-050-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the quantum cohomology ring of any minuscule or commuscule homoge neous space, specialized at q = 1, is semisimple This implies that complex conjugation defines an algebra automorphism of the quantum cohomology ring localized at the quantum parameter We check that this involution coincides with the strange duality defined in our previous article We de duce Vafa-Intriligator type formulas for the Gromov-Witten invariants

引用

页码：1246 / 1263

页数：18

共 14 条

[1] The quantum Euler class and the quantum cohomology of the Grassmannians [J].