The University of Michigan Combinatorics Seminar


Abstract 

The RobinsonSchenstedKnuth (RSK) correspondence is a bijection between tworowed lexicographic arrays and semistandard bitableaux. We will describe a generalization of this correspondence. For any Grassmannian permutation v, we will define a bijection between tworowed lexicographic arrays and vsemistandard bitableaux, where vsemistandard bitableaux are generalizations of semistandard bitableaux whose shapes and contents depend on v. As an application, we will show how this generalization of the RSK correspondence can be used to obtain local properties at the Tfixed point [v] of a Schubert or Richardson variety in the Grassmannian. 