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Discrete Mathematics & Theoretical Computer Science |
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.3095The ABC's of affine Grassmannians and Hall-Littlewood polynomialsArticle
- 1 Department of mathematics [Philadelphie]
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.
Source: HAL:hal-01283121v1
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]
Funding:
- Source : OpenAIRE Graph
- 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
- Combinatorics of affine Schubert calculus, K-theory, and Macdonald polynomials; Funder: National Science Foundation; Code: 1001898
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