Title: Forest polynomials and harmonics for the ideal of quasisymmetric polynomials
| Speaker: | Vasu Tewari |
| Affiliation: | University of Toronto |
| Location: | MC 6029 |
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm.
Abstract: The type A coinvariant algebra, obtained by quotienting the polynomial ring by the ideal of positive degree symmetric polynomials, is a rich and active object of study. A distinguished basis for this quotient is given by Schubert polynomials. There is a dual to this story involving degree polynomials studied in depth by Postnikov-Stanley who shed light on their combinatorics.
I will describe the analogous picture in the context of the quotient of the polynomial ring modulo the ideal of positive degree quasisymmetric polynomials. The Schubert polynomials will be replaced by forest polynomials, while the degree polynomials will be replaced certain volume polynomials. This is joint work with Philippe Nadeau (CNRS and Univ. Lyon).