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 complex reductive algebraic groups, proving that the Betti numbers of regular Hessenberg varieties are palindromic.
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PRECUP, M. THE BETTI NUMBERS OF REGULAR HESSENBERG VARIETIES ARE PALINDROMIC. Transformation Groups 23, 491–499 (2018) doi:10.1007/s00031-017-9442-9