CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Thursday, February 24, 2022 - 3:30pm

Mark Skandera

Lehigh University

Location

University of Pennsylvania

DRL 4C4

For each element $z$ of the symmetric group algebra we define a symmetric generating function $Y(z) = \sum_\lambda \epsilon^\lambda(z) m_\lambda$, where $epsilon^\lambda$ is the induced sign character indexed by $\lambda$. Expanding $Y(z)$ in other symmetric function bases, we obtain other trace evaluations as coefficients. We show that each symmetric function in $\span_Z \{m_\lambda \}$ is $Y(z)$ for some $z$ in $Q[S_n]$, and use this fact to give new interpretations of the permanent of a totally nonnegative matrix. For the full paper, see https://arxiv.org/abs/2010.00458v2.