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- W4386614265 abstract "We relate the mixed Hodge structure on the cohomology of open positroid varieties (in particular, their Betti numbers over $mathbb{C}$ and point counts over $mathbb{F}_q$) to Khovanov--Rozansky homology of associated links. We deduce that the mixed Hodge polynomials of top-dimensional open positroid varieties are given by rational $q,t$-Catalan numbers. Via the curious Lefschetz property of cluster varieties, this implies the $q,t$-symmetry and unimodality properties of rational $q,t$-Catalan numbers. We show that the $q,t$-symmetry phenomenon is a manifestation of Koszul duality for category $mathcal{O}$, and discuss relations with open Richardson varieties and extension groups of Verma modules." @default.
- W4386614265 created "2023-09-12" @default.
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- W4386614265 date "2020-12-17" @default.
- W4386614265 modified "2023-10-18" @default.
- W4386614265 title "Positroids, knots, and $q,t$-Catalan numbers" @default.
- W4386614265 doi "https://doi.org/10.48550/arxiv.2012.09745" @default.
- W4386614265 hasPublicationYear "2020" @default.
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