UW Combinatorics Seminar

Title: Schubert polynomials and Kraskiewicz-Pragacz modules

Masaki Watanabe

Wednesday October 21, 4:00pm-5:10pm
Padelford C-401

Pre-Seminar 3:00pm-3:25pm in PDL C-401

ABSTRACT

Schubert polynomials, first introduced by Lascoux and Schutzenberger, is a family of polynomials describing the Schubert classes (and thus the intersection of Schubert subvarieties) in flag varieties. They contain Schur functions (in a finite number of variables) as their special cases and thus can be seen as a kind of generalizations of Schur functions. Schur functions are known to appear as the characters of irreducible representations of $\operatorname{GL}_n$. 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. In this talk I will talk about my results on Kraskiewicz-Pragacz modules revealing some (old and new) properties of Schubert polynomials. I would also like to talk about my recent study related to this material.



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Sara Billey, Combinatorics Seminar, Mathematics Department, University of Washington

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