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

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.

arXiv comment8 pages, 1 figure. Virtually identical to the version submitted in July 2011. To be contained in the author's doctoral thesis written under the supervision of Robert A. Proctor