“Flipclasses and combinatorial invariance for Kazhdan-Lusztig polynomials”
19 Marzo 2024, ore 12:30 - Aula 2AB40 - Francesco Esposito (Dipartimento di Matematica “Tullio Levi-Civita”)
Abstract
I relate on (ongoing) joint work with Mario Marietti.
We investigate a novel approach to the Combinatorial Invariance Conjecture of Kazhdan–Lusztig polynomials for the symmetric group. Using the new concept of flipclasses, we introduce some combinatorial invariants of intervals in the symmetric group whose analysis leads us to a recipe to compute the coefficients of $q^h$ of the Kazhdan- Lusztig $\tilde{R}$-polynomials, for $h \leq 6$. This recipe depends only on the isomorphism class (as a poset) of the interval indexing the polynomial and thus provides new evidence for the Combinatorial Invariance Conjecture.
If time permits, I will sketch how to generalize the discussion to finite Weyl groups.
