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arXiv math/02012052002-01math.AGmath.RT

A conjectural generalization of n! result to arbitrary groups

Shrawan Kumar, Jesper Funch Thomsen

备注：: Main conjectures has changed, 28 pages

英文摘要：

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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