Speaker:  Linus Setiabrata, University of Chicago
Title: Double orthodontic polynomials
Time: 2:30 PM, Monday, September 23, 2024
Place:  Malott 206

Abstract: Motivated by our search for a representation-theoretic avatar of double Grothendieck polynomials $\mathfrak G_w(\mathbf x; \mathbf y)$, we give a new formula for $\mathfrak G_w(\mathbf x; \mathbf y)$ based on Magyar's orthodontia algorithm for diagrams. We obtain a similar formula for double Schubert polynomials $\mathfrak S_w(\mathbf x; \mathbf y)$, and a curious positivity result: For vexillary permutations $w\in S_n$, the polynomial $x_1^n\dots x_n^n\mathfrak S_w(x_n^{-1}, \dots, x_1^{-1}; 1, \dots, 1)$ is a graded nonnegative sum of Lascoux polynomials. Part of this talk is based on joint work with Avery St. Dizier.


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