OIST Representation Theory Seminar

Date

2021年10月26日 (火) 9:30 10:30

Location

On Zoom

Description

Speaker: George Seelinger, University of Michigan

Title: Diagonal harmonics and shuffle theorems

 

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.

 

Zoom info can be found on the seminar webpage.

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