Department of

Mathematics


Seminar Calendar
for events the day of Thursday, September 16, 2021.

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     August 2021           September 2021          October 2021    
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  1  2  3  4  5  6  7             1  2  3  4                   1  2
  8  9 10 11 12 13 14    5  6  7  8  9 10 11    3  4  5  6  7  8  9
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Thursday, September 16, 2021

3:00 pm in 347 Altgeld Hall,Thursday, September 16, 2021

Grothendieck-to-Lascoux Expansions

Tianyi Yu   [email] (UCSD)

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.