|Date: Friday, October 16, 2015
Location: 4088 East Hall (3:10 PM to 4:00 PM)
Title: Schubert polynomials and Kraskiewicz-Pragacz modules
Abstract: Schubert polynomials, first introduced by Lascoux and Schutzenberger, are a family of polynomials describing the Schubert classes (and thus intersections of Schubert subvarieties) in flag varieties. They include Schur polynomials as special cases and consequently can be viewed as a generalization of Schur functions.
Schur functions are known to appear as characters of irreducible representations of GL_n. Generalising Schur functions to Schubert polynomials, Kraskiewicz and Pragacz introduced modules over the group of upper-triangular matrices whose characters are given by Schubert polynomials. I will talk about my results on Kraskiewicz-Pragacz modules, which reveal some (old and new) properties of Schubert polynomials. I would also like to talk about my recent study related to this material.
Speaker: Masaki Watanabe
Institution: U. Tokyo