October 22, 2024
10:20AM - 11:15AM
Math Tower (MW) 154
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2024-10-22 10:20:00
2024-10-22 11:15:00
Algebraic Geometry Seminar - Linus Setiabrata
Linus SetiabrataUniversity of ChicagoTitleDouble orthodontia formulas and Lascoux positivityAbstractDouble Grothendieck polynomials G_w(x;y) are lifts of structure sheaves of Schubert varieties in the equivariant K-theory of the flag variety. Motivated by our search for a representation-theoretic avatar for these polynomials, we give a new formula for G_w(x;y) based on Magyar's orthodontia algorithm for diagrams. We obtain a similar formula for double Schubert polynomials S_w(x;y), and a curious positivity result: For vexillary permutations w, the polynomial x_1^n \dots x_n^n S_w(x_n^{-1}, \dots, x_1^{-1}; 1, \dots, 1) is a graded nonnegative sum of Lascoux polynomials. This is joint work with Avery St. Dizier.For More Information About the Seminar
Math Tower (MW) 154
OSU ASC Drupal 8
ascwebservices@osu.edu
America/New_York
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Date Range
2024-10-22 10:20:00
2024-10-22 11:15:00
Algebraic Geometry Seminar - Linus Setiabrata
Linus SetiabrataUniversity of ChicagoTitleDouble orthodontia formulas and Lascoux positivityAbstractDouble Grothendieck polynomials G_w(x;y) are lifts of structure sheaves of Schubert varieties in the equivariant K-theory of the flag variety. Motivated by our search for a representation-theoretic avatar for these polynomials, we give a new formula for G_w(x;y) based on Magyar's orthodontia algorithm for diagrams. We obtain a similar formula for double Schubert polynomials S_w(x;y), and a curious positivity result: For vexillary permutations w, the polynomial x_1^n \dots x_n^n S_w(x_n^{-1}, \dots, x_1^{-1}; 1, \dots, 1) is a graded nonnegative sum of Lascoux polynomials. This is joint work with Avery St. Dizier.For More Information About the Seminar
Math Tower (MW) 154
Department of Mathematics
math@osu.edu
America/New_York
public
Linus Setiabrata
University of Chicago
Title
Double orthodontia formulas and Lascoux positivity
Abstract
Double Grothendieck polynomials G_w(x;y) are lifts of structure sheaves of Schubert varieties in the equivariant K-theory of the flag variety. Motivated by our search for a representation-theoretic avatar for these polynomials, we give a new formula for G_w(x;y) based on Magyar's orthodontia algorithm for diagrams. We obtain a similar formula for double Schubert polynomials S_w(x;y), and a curious positivity result: For vexillary permutations w, the polynomial x_1^n \dots x_n^n S_w(x_n^{-1}, \dots, x_1^{-1}; 1, \dots, 1) is a graded nonnegative sum of Lascoux polynomials. This is joint work with Avery St. Dizier.
