BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:George Seelinger (University of Michigan) DTSTART:20211026T003000Z DTEND:20211026T013000Z DTSTAMP:20260423T021219Z UID:OISTRTS/23 DESCRIPTION:Title: Diagonal harmonics and shuffle theorems\nby George Seelinger (Univers ity of Michigan) as part of OIST representation theory seminar\n\n\nAbstra ct\nThe Shuffle Theorem\, conjectured by Haglund\, Haiman\, Loehr\, Remmel and Ulyanov\, and proved by Carlsson and Mellit\, describes the character istic of the $S_n$-module of diagonal harmonics as a weight generating fun ction over labeled Dyck paths under a line with slope −1. The Shuffle Th eorem has been generalized in many different directions\, producing a numb er of theorems and conjectures. We provide a generalized shuffle theorem f or paths under any line with negative slope using different methods from p revious 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 Conjectu re\, yet another generalization of the original Shuffle Conjecture.\n LOCATION:https://researchseminars.org/talk/OISTRTS/23/ END:VEVENT END:VCALENDAR