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The Betti numbers of regular Hessenberg varieties are palindromic. (English) Zbl 1423.20053

Summary: Recently P. Brosnan and T. Y. Chow [Adv. Math. 329, 955–1001 (2018; Zbl 1410.05222)] have proven a conjecture of J. Shareshian and M. L. Wachs [Adv. Math. 295, 497–551 (2016; Zbl 1334.05177)] describing a representation of the symmetric group on the cohomology of regular semisimple Hessenberg varieties for \(\mathrm{GL}_n(\mathbb C)\). A key component of their argument is that the Betti numbers of regular Hessenberg varieties for \(\mathrm{GL}_n(\mathbb C)\) are palindromic. In this paper, we extend this result to all complex reductive algebraic groups, proving that the Betti numbers of regular Hessenberg varieties are palindromic.

MSC:

20G05 Representation theory for linear algebraic groups
14L30 Group actions on varieties or schemes (quotients)
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References:

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