A conjectural generalization of n! result to arbitrary groups

Details A conjectural generalization of n! result to arbitrary groups A conjectural generalization of n! result to arbitrary groups

2002-01-22

arxiv.org/abs/math/0201205v2

Mathematics

Algebraic Geometry

Main conjectures has changed, 28 pages

Scientific paper

We 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.

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