The equivariant cohomology rings of Peterson varieties

被引：9

作者：

Fukukawa, Yukiko ^{[1
]}

Harada, Megumi ^{[2
]}

Masuda, Mikiya ^{[1
]}

机构：

[1] Osaka City Univ, Dept Math, Sumiyoshi Ku, Osaka 5588585, Japan

[2] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4K1, Canada

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2015年 / 67卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

equivariant cohomology; Peterson variety; flag variety; regular sequence;

D O I：

10.2969/jmsj/06731147

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main result of this note gives an efficient presentation of the S-1-equivariant cohomology ring of Peterson varieties (in type A) as a quotient of a polynomial ring by an ideal J, in the spirit of the well-known Borel presentation of the cohomology of the flag variety. Our result simplifies previous presentations given by Harada-Tymoczko and Bayegan-Harada. In particular, our result gives an affirmative answer to a conjecture of Bayegan and Harada that the defining ideal J is generated by quadratics.

引用

页码：1147 / 1159

页数：13

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