The University of Michigan Combinatorics Seminar
Fall 2008
November 14, 4:10-5:00, 3866 East Hall



The shifted plactic monoid

Luis Serrano

University of Michigan


Abstract

We introduce a shifted analog of the plactic monoid of Lascoux and Schützenberger, the shifted plactic monoid. It can be defined in two different ways: via the shifted Knuth relations, or using Haiman's mixed insertion.

Applications include: a new combinatorial derivation (and a new version of) the shifted Littlewood-Richardson Rule; similar results for the coefficients in the Schur expansion of a Schur P-function; and a shifted counterpart of the theory of noncommutative Schur functions in plactic variables.