Combinatorics Seminar: "The Coxeter-Sylvester correspondence and a refinement of Schubert polynomials"
Speaker: Vasu Tewari, University of Hawaii
Abstract: Motivated by computing the class of the permutahedral variety in terms of Schubert classes, we introduce the Coxeter-Sylvester correspondence on words. This correspondence yields a basis for the polynomial ring refining Schubert polynomials.
This new basis has some nice properties -- notably a positive multiplication rule with a combinatorial description. More importantly for us, it is easy to reduce these basis elements modulo the ideal of positive degree quasisymmetric polynomials, which in turn allows us to give a manifestly nonnegative integral description for the coefficients in the Schubert-positivity problem posed at the beginning.
Joint work with Philippe Nadeau (CNRS and Université Lyon 1).
Host: Martha Precup