Combinatorics Seminar: Mikhail Mazin, KSU, speaks on "Combinatorics and geometry of partial flag varieties and the quantum group."
Mikhail Mazin, Kansas State University
Title: Combinatorics and geometry of partial flag varieties and the quantum group (following Beilinson-Lusztig-Macpherson paper from 1990)
Abstract: In their almost 30 years old paper, Beilinson, Lusztig, and Macpherson used the space Fl(n,d)xFl(n,d) of pairs of n-step partial flags in a d-dimentional vector space to describe a geometric framework for the quantum group of Gl(n). It turns out that the space of linear combinations of Gl(d) orbits in Fl(n,d)xFl(n,d),endowed with a convolution product is a quotient of the quantum group, and that as d goes to infinity the appropriately defined "limit" of this quotient is the whole quantum group.
In this talk I will focus on the combinatorics of the Gl(d) orbits in the space of pairs of flags. Turns out that the orbits are enumerated by nxn matrices with non-negative integer entries. I will talk about the Bruhat order on such matrices, dimensions of the corresponding orbits, and combinatorial formulas for the convolution product. Time permitting, I will also explain how one gets a surjective map from the quantum group.
Wednesday, September 18, 2019 at 3:30pm to 4:20am
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