Avinash J. Dalal ; Jennifer Morse
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A t-generalization for Schubert Representatives of the Affine Grassmannian
dmtcs:2371 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2013,
DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
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https://doi.org/10.46298/dmtcs.2371
A t-generalization for Schubert Representatives of the Affine GrassmannianConference paper
Authors: Avinash J. Dalal 1; Jennifer Morse 1
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Avinash J. Dalal;Jennifer Morse
1 Department of mathematics [Philadelphie]
We introduce two families of symmetric functions with an extra parameter t that specialize to Schubert representatives for cohomology and homology of the affine Grassmannian when t=1. The families are defined by a statistic on combinatorial objects associated to the type-A affine Weyl group and their transition matrix with Hall-Littlewood polynomials is t-positive. We conjecture that one family is the set of k-atoms.
Thomas Lam;Luc Lapointe;Jennifer Morse;Anne Schilling;Mark Shimozono;et al., Fields Institute monographs, Primer on k-Schur Functions, pp. 9-131, 2014, 10.1007/978-1-4939-0682-6_2.