The odd Littlewood-Richardson rule

被引：4

作者：

Ellis, Alexander P. ^{[1
]}

机构：

[1] Columbia Univ, Dept Math, New York, NY 10027 USA

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2013年 / 37卷 / 04期

关键词：

Symmetric functions; Hopf algebras; Supalgebra; Odd symmetric functions; Hives; Littlewood-Richardson; Schubert calculus; HECKE ALGEBRAS;

D O I：

10.1007/s10801-012-0389-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In previous work with Mikhail Khovanov and Aaron Lauda we introduced two odd analogues of the Schur functions: one via the combinatorics of Young tableaux (odd Kostka numbers) and one via an odd symmetrization operator. In this paper we introduce a third analogue, the plactic Schur functions. We show they coincide with both previously defined types of Schur function, confirming a conjecture. Using the plactic definition, we establish an odd Littlewood-Richardson rule. We also re-cast this rule in the language of polytopes, via the Knutson-Tao hive model.

引用

页码：777 / 799

页数：23

共 22 条

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[2]

Buch A.S., 2000, ENSEIGN MATH, V2, P43

[3]

Ellis A.P, 2011, ARXIV 1111 1320

[4] The Hopf algebra of odd symmetric functions [J].