A conjectural generalization of n! result to arbitrary groups

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63172We relate the n! conjecture (by Garsia and Haiman) to the geometry of principal nilpotent pairs, and state a conjecture generalizing the n! conjecture to arbitrary semisimple algebraic groups. We also show, using Borel's fixed point theorem, how to reduce the n! conjecture to staircase partitions. Finally we study the interplay between characteristic p and the n! conjecture for box partitions.Main conjectures has changed, 28 pagesAlgebraic GeometryRepresentation TheoryA conjectural generalization of n! result to arbitrary groupstext