On some quadratic algebras, Dunkl elements and type A flag varieties

Time：2023-01-05 Thu 15:00-16:30

Venue：Venue: TSIMF Zoom: 482 240 1589（PW: BIMSA）

Speaker：Anatol Kirillov BIMSA

Abstract

We introduce certain class of quadratic algebras together with commutative subalgebras generated by additive and multiplicative Dunkl elements correspondingly. We identify these subalgebras with cohomology and K-theories of type A flag varieties. We show that value of Schubert polynomials on additive Dunkl elements is a generating function for the corresponding Littlewood-Richardson coefficients. We state some open problems related with our quadratic algebras. (work partly joint with S Fomin)

DATEJanuary 5, 2023

Related News

0
Algebraic Combinatorics Seminar | On some quadratic algebras, Dunkl elements and type A flag varieties
AbstractWe introduce certain class of quadratic algebras together with commutative subalgebras generated by additive and multiplicative Dunkl elements correspondingly. We identify these subalgebras with cohomology and K-theories of type A flag varieties. We show that value of Schubert polynomials on additive Dunkl elements is a generating function for the corresponding Littlewood-Richardson coe...
1
On the full Kostant-Toda lattice and the flag varieties
AbstractIn 1967, Japanese physicist Morikazu Toda proposed an integrable lattice model to describe motions of a chain of particles with exponential interactions between nearest neighbors. Since then, Toda lattice and its generalizations have become the test models for various techniques and philosophies in integrable systems and wide connections are built with many other branches of mathematics...