THE BETTI NUMBERS OF REGULAR HESSENBERG VARIETIES ARE PALINDROMIC

Martha Precup

doi:10.1007/s00031-017-9442-9

THE BETTI NUMBERS OF REGULAR HESSENBERG VARIETIES ARE PALINDROMIC

Martha Precup

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

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 complex reductive algebraic groups, proving that the Betti numbers of regular Hessenberg varieties are palindromic.

Original language	English
Pages (from-to)	491-499
Number of pages	9
Journal	Transformation Groups
Volume	23
Issue number	2
DOIs	https://doi.org/10.1007/s00031-017-9442-9
State	Published - Jun 1 2018

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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 GLn(ℂ). A key component of their argument is that the Betti numbers of regular Hessenberg varieties for GLn(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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AB - 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 GLn(ℂ). A key component of their argument is that the Betti numbers of regular Hessenberg varieties for GLn(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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THE BETTI NUMBERS OF REGULAR HESSENBERG VARIETIES ARE PALINDROMIC

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