A conjectural generalization of n! result to arbitrary groups

2002/01/22 by Shrawan Kumar, Kumar, Shrawan, Jesper Funch Thomsen +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #math.AG #math.RT

paper · pdf · doi:10.48550/arxiv.math/0201205

Main conjectures has changed, 28 pages

arxiv created 2002/08/14 · arxiv updated 2009/11/30

Abstract

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.

Citations

• Algebraic Families on an Algebraic Surface

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