Avinash J. Dalal ; Jennifer Morse
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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)
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https://doi.org/10.46298/dmtcs.3095
The ABC's of affine Grassmannians and Hall-Littlewood polynomials
Authors: Avinash J. Dalal 1; Jennifer Morse 1
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Avinash J. Dalal;Jennifer Morse
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.