DOI: 10.5802/alco.519 ISSN: 2589-5486

Counting points on Hessenberg varieties over finite fields

Alex Abreu, Antonio Nigro, Samrith Ram
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We give a counting formula in terms of modified Hall–Littlewood polynomials and the chromatic quasisymmetric function for the number of points on an arbitrary Hessenberg variety over a finite field. As a consequence, we express the Poincaré polynomials of complex Hessenberg varieties in terms of a Hall scalar product involving the symmetric functions above. We use these results to give a new proof of a combinatorial formula for the modified Hall–Littlewood polynomials.

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