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The $P=W$ conjecture for $\mathrm{GL}_n$

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arxiv 2209.02568 v2 pith:G6LHQPJV submitted 2022-09-06 math.AG math.RT

Davesh Maulik , Junliang Shen This is my paper · ORCID
classification math.AGmath.RT
keywords conjecturemathrmperversityprovetheoremapplyarbitraryclasses
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abstract

We prove the $P=W$ conjecture for $\mathrm{GL}_n$ for all ranks $n$ and curves of arbitrary genus $g\geq 2$. The proof combines a strong perversity result on tautological classes with the curious Hard Lefschetz theorem of Mellit. For the perversity statement, we apply the vanishing cycles constructions in our earlier work to global Springer theory in the sense of Yun, and prove a parabolic support theorem.

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  1. A geometric interpretation of the Delta Conjecture

    math.CO 2024-12 conditional novelty 7.0 of 10

    The Delta Conjecture symmetric function is realized as the bigraded Frobenius character of the Borel-Moore homology of a new family of affine Springer fibers.

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