Diagonal harmonics and shuffle theorems
George Seelinger (University of Michigan)
Abstract: The Shuffle Theorem, conjectured by Haglund, Haiman, Loehr, Remmel and Ulyanov, and proved by Carlsson and Mellit, describes the characteristic of the $S_n$-module of diagonal harmonics as a weight generating function over labeled Dyck paths under a line with slope −1. The Shuffle Theorem has been generalized in many different directions, producing a number of theorems and conjectures. We provide a generalized shuffle theorem for paths under any line with negative slope using different methods from previous proofs of the Shuffle Theorem. In particular, our proof relies on showing a "stable" shuffle theorem in the ring of virtual GL_l-characters. Furthermore, we use our techniques to prove the Extended Delta Conjecture, yet another generalization of the original Shuffle Conjecture.
combinatoricsquantum algebrarings and algebrasrepresentation theory
Audience: researchers in the topic
OIST representation theory seminar
Series comments: Timings of this seminar may vary from week to week.
Organizer: | Liron Speyer* |
*contact for this listing |