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 GrassmannianArticle
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.
Combinatorics of affine Schubert calculus, K-theory, and Macdonald polynomials; Funder: National Science Foundation; Code: 1001898
Bibliographic References
2 Documents citing this article
Michael Chmutov;Joel Brewster Lewis;Pavlo Pylyavskyy, 2022, Monodromy in Kazhdan–Lusztig cells in affine type A, arXiv (Cornell University), 386, 3-4, pp. 1891-1949, 10.1007/s00208-022-02434-4, https://arxiv.org/abs/1706.00471.
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.