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Formality and Lusztig’s Generalized Springer Correspondence

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Abstract

We prove a derived equivalence between each block of the derived category of sheaves on the nilpotent cone and the category of differential graded modules over a degeneration of Lusztig’s graded Hecke algebra. Along the way, we construct and study a mixed version of the geometric category. This work can be viewed as giving a derived version of the generalized Springer correspondence.

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Acknowledgements

We are very grateful to George Lusztig for answering questions about his work; in particular, for pointing us to [22, Proposition 4.7]. We also thank Jay Taylor for explaining the proofs in Section 3.1. We also thank Matt Douglass and Pramod Achar for helpful discussions. Finally we thank several anonymous referees for their helpful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, University of Georgia, Athens, GA, 30602, USA

    Laura Rider

  2. Department of Mathematics and Actuarial Science, Butler University, Indianapolis, IN, 46208, USA

    Amber Russell

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  1. Laura Rider
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  2. Amber Russell
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Correspondence to Laura Rider.

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Presented by: Pramod Achar

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L.R. was supported by an NSF Postdoctoral Research Fellowship.

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Rider, L., Russell, A. Formality and Lusztig’s Generalized Springer Correspondence. Algebr Represent Theor 24, 699–714 (2021). https://doi.org/10.1007/s10468-020-09966-w

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