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 Grassmannian
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.
Plethystic Formulas for Macdonaldq, t-Kostka Coefficients
2 Documents citing this article
Source : OpenCitations
Chmutov, Michael; Lewis, Joel Brewster; Pylyavskyy, Pavlo, 2022, Monodromy In KazhdanâLusztig Cells In Affine Type A, Mathematische Annalen, 10.1007/s00208-022-02434-4.
Lam, Thomas; Lapointe, Luc; Morse, Jennifer; Schilling, Anne; Shimozono, Mark; Zabrocki, Mike, 2014, Primer On k-Schur Functions, k-Schur Functions And Affine Schubert Calculus, pp. 9-131, 10.1007/978-1-4939-0682-6_2.