Algebra and Number Theory Seminar
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Posted October 17, 2020
Last modified October 18, 2020
Jianping Pan, University of California, Davis
Crystal for stable Grothendieck polynomials
The Grothendieck polynomials arise from enumerative geometry, as they can be used to calculate the intersection numbers for the Flag varieties. We introduce a crystal on decreasing factorizations of 321-avoiding elements of the 0-Hecke monoid, whose generating functions are the stable Grothendieck polynomials. This crystal is a K-theoretic generalization of the Morse-Schilling crystal on decreasing factorizations in the symmetric group. We prove that it intertwines with the crystal on set-valued tableaux introduced by Monical, Pechenik, and Scrimshaw (through the residue map). We also define a new insertion algorithm that intertwines with our crystal, with surprising connections to the Hecke insertion algorithm and the uncrowding algorithm for set-valued tableaux.
This talk is based on joint work arXiv:1911.08732 with Jennifer Morse, Wencin Poh, and Anne Schilling.
Harmonic Analysis Seminar
Abstract and additional information
Posted October 8, 2020
3:30 pm - 4:30 pm https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09 Originally scheduled for 3:30 pm, Wednesday, October 14, 2020
Nicholas J Christoffersen, LSU
TBA