Catalania

Abstract: Many well-known formulas in symmetric function theory such as those for Hall-Littlewood polynomials and the Weyl character formula involve a product over all positive roots. Replacing this product with one over an upper order ideal of positive roots (of which there are Catalan many) yields new families of polynomials. We will see how this idea leads to elegant formulas for $k$-Schur functions, their $K$-theoretic versions, $\nabla s_\lambda$, and Macdonald polynomials, and explore how such formulas can pave the way to positive combinatorics.

algebraic geometrycombinatorics

Audience: researchers in the discipline

MAAGC 2023

Series comments: The eighth annual Mid-Atlantic Algebra, Geometry, and Combinatorics (MAAGC) Workshop will take place Friday and Saturday, December 1-2, 2023 at Virginia Commonwealth University in Richmond, Virginia.

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-1728937.