The Betti numbers of regular Hessenberg varieties are palindromic

2016/03/24 by Precup, Martha · 2 citations
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1603.07662

Abstract

Recently Brosnan and Chow have proven a conjecture of Shareshian and Wachs describing a representation of the symmetric group on the cohomology of regular semisimple Hessenberg varieties for GL_n(ℂ). A key component of their argument is that the Betti numbers of regular Hessenberg varieties for GL_n(ℂ) are palindromic. In this paper, we extend this result to all reductive algebraic groups, proving that the Betti numbers of regular Hessenberg varieties are palindromic.

Cited by

• Restricted inversion polynomials
• Notes on the cohomology of partial Hessenberg varieties

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