## On the affine Hecke category for SL(3)

Joint with Leo Patimo. We find a surprisingly beautiful basis of the Hom spaces between indecomposable Soergel bimodules for SL(3) (something that we call "indecomposable light leaves").

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# Featured papers and preprints

## Highlighted Papers

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On the affine Hecke category for SL(3)

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Gentle introduction to Soergel bimodules I: The basics

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Light leaves and Lusztig’s conjecture

Joint with Leo Patimo. We find a surprisingly beautiful basis of the Hom spaces between indecomposable Soergel bimodules for SL(3) (something that we call "indecomposable light leaves").

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July 1, 2020

** Sao Paulo Journal of Mathematical Sciences**, 13(2) (2019), 499-538. This paper is the first of a series of introductory papers on the fascinating world of Soergel bimodules. It is combinatorial in nature and should be accessible to a broad audience.

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September 1, 2017

**Advances in Mathematics **(2015) 772-807.
I prove that Lusztig's conjecture reduces to a problem about the light leaves. Using the result in Section 4.3 of this paper Geordie Williamson **disproved Lusztig's conjecture!** The counterexamples grow exponentially in the Coxeter number. Here is Geordie's paper

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January 1, 2015