A Direct Way to Find the Right Key of a Semistandard Young Tableau

TL;DR

This paper introduces direct, inspection-based methods to determine the right and left keys of semistandard Young tableaux, simplifying the process of computing Demazure characters without auxiliary combinatorial objects.

Contribution

It presents novel, straightforward techniques for finding tableau keys directly, improving computational efficiency over previous methods that relied on additional combinatorial structures.

Findings

Methods enable direct key extraction by inspection

Simplifies computation of Demazure characters

Eliminates need for auxiliary combinatorial objects

Abstract

The right and left key of a semistandard Young tableau were introduced by Lascoux and Schutzenberger in 1990. Most prominently, the right key is a tool used to find Demazure characters for sl(n,C). Previous methods used to compute these keys require introducing other types of combinatorial objects. This paper gives methods to obtain the right and left keys by inspection of the semistandard Young tableau.