Crystal chute moves on pipe dreams

Abstract: Schubert polynomials represent a basis for the cohomology of the complete flag variety. In this context, Schubert polynomials are generating functions over various combinatorial objects, such as rc-graphs or reduced pipe dreams. By restricting Bergeron and Billey’s chute moves on rc-graphs, we define a Demazure crystal structure on the monomials of a Schubert polynomial. As a consequence, we provide a new method for decomposing Schubert polynomials as sums of key polynomials. These results complement related work of Assaf and Schilling via reduced factorizations with cutoff, as well as Lenart’s coplactic operators on biwords. No prior knowledge of either key polynomials or crystals will be assumed in this talk.

algebraic geometrycombinatorics

Audience: researchers in the discipline

MAAGC 2024

Series comments: The 2024 annual Mid-Atlantic Algebra, Geometry, and Combinatorics (MAAGC) Workshop will take place Friday and Saturday, October 11-12, 2024 at The George Washington University in Washington, DC.

The MAAGC Workshop aims to bring together senior researchers and junior mathematicians from the region to exchange ideas and forge collaborations in algebra, geometry, and combinatorics. The conference is funded by National Science Foundation grant DMS-2408985.