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Mixed Perverse Sheaves on Flag Varieties for Coxeter Groups

  • Pramod N. Achar (a1), Simon Riche (a2) and Cristian Vay (a3)

In this paper we construct an abelian category of mixed perverse sheaves attached to any realization of a Coxeter group, in terms of the associated Elias–Williamson diagrammatic category. This construction extends previous work of the first two authors, where we worked with parity complexes instead of diagrams, and we extend most of the properties known in this case to the general setting. As an application we prove that the split Grothendieck group of the Elias–Williamson diagrammatic category is isomorphic to the corresponding Hecke algebra, for any choice of realization.

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Author P.A. was partially supported by NSF Grant No. DMS-1500890. Author S.R. was partially supported by ANR Grant No. ANR-13-BS01-0001-01. This project received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 677147). The work of Author C.V. was done during a research stay at the Université Clermont Auvergne supported by CONICET. He also was partially supported by Secyt (UNC), FONCyT PICT 2016-3957 and MathAmSud project GR2HOPF.

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Canadian Journal of Mathematics
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