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Local Hodge theory of Soergel bimodules

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Acta Mathematica

Abstract

We prove the local hard Lefschetz theorem and local Hodge–Riemann bilinear relations for Soergel bimodules. Using results of Soergel and Kübel, one may deduce an algebraic proof of the Jantzen conjectures. We observe that the Jantzen filtration may depend on the choice of non-dominant regular deformation direction.

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Authors and Affiliations

  1. University of Sydney, School of Mathematics and Statistics, Carslaw Building F07, Sydney, NSW, 2006, Australia

    Geordie Williamson

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  1. Geordie Williamson
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Correspondence to Geordie Williamson.

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Dedicated to Ben and Yeppie.

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Williamson, G. Local Hodge theory of Soergel bimodules. Acta Math 217, 341–404 (2016). https://doi.org/10.1007/s11511-017-0146-8

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  • DOI: https://doi.org/10.1007/s11511-017-0146-8

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