Genomic tableaux

被引：16
|
作者：
Pechenik, Oliver [1 ]
Yong, Alexander [2 ]
机构：
[1] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA
[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA
来源：
JOURNAL OF ALGEBRAIC COMBINATORICS | 2017年 / 45卷 / 03期
基金：
美国国家科学基金会;
关键词：
INCREASING TABLEAUX; K-THEORY; POSITIVITY; COHOMOLOGY; RULES;
D O I：
10.1007/s10801-016-0720-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We explain how genomic tableaux [Pechenik-Yong '15] are a semistandard complement to increasing tableaux [Thomas-Yong '09]. From this perspective, one inherits genomic versions of jeu de taquin, Knuth equivalence, infusion and Bender-Knuth involutions, as well as Schur functions from (shifted) semistandard Young tableaux theory. These are applied to obtain new Littlewood-Richardson rules for K-theory Schubert calculus of Grassmannians (after [Buch '02]) and maximal orthogonal Grassmannians (after [Clifford-Thomas-Yong '14], [Buch-Ravikumar '12]). For the unsolved case of Lagrangian Grassmannians, sharp upper and lower bounds using genomic tableaux are conjectured.
引用
收藏
页码：649 / 685
页数：37
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