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Algebra, Geometry & Combinatorics: Grothendieck-to-Lascoux Expansions

Event Type
Seminar/Symposium
Sponsor
N/A
Location
347 Altgeld Hall
Date
Sep 16, 2021   3:00 pm  
Speaker
Tianyi Yu (UCSD)
Contact
Colleen Robicheaux
E-Mail
cer2@uiuc.edu
Views
26

Abstract: We establish the conjecture of Reiner and Yong for an explicit combinatorial formula for the expansion of a Grothendieck polynomial into the basis of Lascoux polynomials. This expansion is a subtle refinement of its symmetric function version due to Buch, Kresch, Shimozono, Tamvakis, and Yong, which gives the expansion of stable Grothendieck polynomials indexed by permutations into Grassmannian stable Grothendieck polynomials. Our expansion is the K-theoretic analogue of that of a Schubert polynomial into Demazure characters, whose symmetric analogue is the expansion of a Stanley symmetric function into Schur functions. Our expansions extend to flagged Grothendieck polynomials. This is a joint work with Mark Shimozono.

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