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A $t$-generalization for Schubert Representatives of the Affine Grassmannian

Abstract : 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.
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https://hal.inria.fr/hal-01229689
Contributor : Alain Monteil <>
Submitted on : Tuesday, November 17, 2015 - 10:19:59 AM
Last modification on : Friday, June 28, 2019 - 1:40:04 PM
Long-term archiving on: : Thursday, February 18, 2016 - 11:39:06 AM

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Avinash J. Dalal, Jennifer Morse. A $t$-generalization for Schubert Representatives of the Affine Grassmannian. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.1125-1136. ⟨hal-01229689⟩

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