Avinash J. Dalal ; Jennifer Morse - 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) - 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

  • 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.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: $k$-Schur functions,Pieri rule,Bruhat order,Hall-Littlewood polynomials,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Combinatorics of affine Schubert calculus, K-theory, and Macdonald polynomials; Funder: National Science Foundation; Code: 1001898

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