Title: The quasisymmetric Macdonald polynomials are quasi-Schur positive at t = 0
| Speaker | Harper Niergarth and Kartik Singh |
| Affiliation | University of Waterloo |
| Location | MC 5479 |
Abstract: The quasisymmetric Macdonald polynomials G_\gamma (X; q, t) are a quasisymmetric refinement of the symmetric Macdonald polynomials that specialize to the quasisymmetric Schur functions QS_\alpha (X). We study the t = 0 specialization G_\gamma (X; q,0), which can be described as a sum over weighted multiline queues. We show that G_\gamma (X; q, 0) expands positively in the quasisymmetric Schur basis and give a charge formula for the quasisymmetric Kostka-Foulkes polynomials K_{\gamma,\alpha}(q) in the expansion G_\gamma (X; q, 0) = \sum K_{\gamma,\alpha}(q) QS_\alpha(X). The proof relies heavily on crystal operators, and if you do not know what that means, come find out! This is joint work with Olya Mandelshtam.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm,