A survey of recent developments on Hessenberg varieties

Abstract

This article surveys recent developments on Hessenberg varieties, emphasizing some of the rich connections of their cohomology and combinatorics. In particular, we will see how hyperplane arrangements, representations of symmetric groups, and Stanley's chromatic symmetric functions are related to the cohomology rings of Hessenberg varieties. We also include several other topics on Hessenberg varieties to cover recent developments.

arXiv comment24 pages, 14 figures

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Cited by in corpus (3)

• The permutahedral variety, mixed Eulerian numbers, and principal specializations of Schubert polynomials
• Positivity of Peterson Schubert Calculus
• An additive basis for the cohomology rings of regular nilpotent Hessenberg varieties