## Avinash J. Dalal ; Jennifer Morse - The ABC's of affine Grassmannians and Hall-Littlewood polynomials

dmtcs:3095 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) - https://doi.org/10.46298/dmtcs.3095
The ABC's of affine Grassmannians and Hall-Littlewood polynomials

Authors: Avinash J. Dalal ; Jennifer Morse

We give a new description of the Pieri rule for $k$-Schur functions using the Bruhat order on the affine type-$A$ Weyl group. In doing so, we prove a new combinatorial formula for representatives of the Schubert classes for the cohomology of affine Grassmannians. We show how new combinatorics involved in our formulas gives the Kostka-Foulkes polynomials and discuss how this can be applied to study the transition matrices between Hall-Littlewood and $k$-Schur functions.

Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Imported on: January 31, 2017
Keywords: Bruhat order, Macdonald polynomials, Hall-Littlewood polynomials, $k$-tableaux,$k$-Schur functions, Pieri rule,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Fundings :
Source : OpenAIRE Research Graph
• Combinatorics of affine Schubert calculus, K-theory, and Macdonald polynomials; Funder: National Science Foundation; Code: 1001898
• FRG: Collaborative Research: Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects; Funder: National Science Foundation; Code: 0652641
• Refined symmetric functions and affine analogs in combinatorics; Funder: National Science Foundation; Code: 0638625