Uniform bases for ideal arrangements

2019/12/05 by Enokizono, Makoto, Horiguchi, Tatsuya, Nagaoka, Takahiro +1 · 1 citation
#14M15 #17B22 #32S22 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1912.02448

Abstract

In this paper we introduce and study uniform bases for the ideal arrangements in all Lie types. Explicit uniform bases are given by Abe-Horiguchi-Masuda-Murai-Sato for types A,B,C,G and we provide them for other types. Combining the explicit uniform bases with the work of Abe-Horiguchi-Masuda-Murai-Sato, we also obtain explicit presentations of the cohomology rings of regular nilpotent Hessenberg varieties in all Lie types.

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• Notes on the cohomology of partial Hessenberg varieties

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• Hessenberg varieties and hyperplane arrangements
• A filtration on the cohomology rings of regular nilpotent Hessenberg varieties
• A survey of recent developments on Hessenberg varieties
• Arrangements of ideal type