The octahedron recurrence and gln crystals

被引：19

作者：

Henriques, Andre

Kamnitzer, Joel

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

来源：

ADVANCES IN MATHEMATICS | 2006年 / 206卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

crystals; octahedron recurrence; hives; coboundary category;

D O I：

10.1016/j.aim.2005.08.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the hive model of gl(n) tensor products, following Knutson, Tao, and Woodward. We define a coboundary category where the tensor product is given by hives and where the associator and commutor are defined using a modified octahedron recurrence. We then prove that this category is equivalent to the category of crystals for the Lie algebra 91, The proof of this equivalence uses a new connection between the octahedron recurrence and the Jeu de Taquin and Schutzenberger involution procedures on Young tableaux. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：211 / 249

页数：39

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[2]

Fulton W., 1997, LONDON MATH SOC STUD, V35

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