SCHUBERT CALCULUS AND TORSION EXPLOSION

被引：54

作者：

Williamson, Geordie ^{[1
]}

Kontorovich, Alex ^{[2
]}

McNamara, Peter J. ^{[3
]}

机构：

[1] Max Planck Inst Math, Vivatsgasse 7, D-53111 Bonn, Germany

[2] Rutgers State Univ, New Brunswick, NJ USA

[3] Univ Queensland, Brisbane, Qld, Australia

来源：

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 30卷 / 04期

基金：

美国国家科学基金会;

关键词：

KAZHDAN-LUSZTIG CONJECTURE; AFFINE LIE-ALGEBRAS; INTERSECTION COHOMOLOGY; REPRESENTATION-THEORY; COMBINATORICS; MODULES; SHEAVES;

D O I：

10.1090/jams/868

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The author observes that certain numbers occurring in Schubert calculus for SLn also occur as entries in intersection forms controlling decompositions of Soergel bimodules in higher rank. These numbers grow exponentially. This observation gives many counter-examples to the expected bounds in Lusztig’s conjecture on the characters of simple rational modules for SLn over fields of positive characteristic. The examples also give counter-examples to the James conjecture on decomposition numbers for symmetric groups. © 2016 American Mathematical Society.

引用

页码：1023 / 1046

页数：24

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