Seminar - Ricky Liu

Subalgebras of the Fomin-Kirillov Algebra

Abstract: 

One of the main unsolved problems in Schubert calculus is to give a combinatorial formula for the structure constants in the cohomology of the flag variety. Fomin and Kirillov introduced a noncommutative quadratic algebra in which the existence of certain monomial expansions would yield a solution to this problem. I will discuss recent efforts towards understanding the structure of the Fomin-Kirillov algebra. In particular, I will describe certain subalgebras that are surprisingly well-behaved and have properties analogous to those of finite Coxeter groups, which  suggests that they are worthy of independent interest. This is joint work with Jonah Blasiak and Karola Meszaros.