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arXiv · 1603.07662

The Betti numbers of regular Hessenberg varieties are palindromic

Martha Precup
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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 $GL_n(\mathbb{C})$. A key component of their argument is that the Betti numbers of regular Hessenberg varieties for $GL_n(\mathbb{C})$ 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.

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Martha Precup. 2016-03-24. The Betti numbers of regular Hessenberg varieties are palindromic. https://arxiv.org/abs/1603.07662

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