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Mixed Perverse Sheaves on Flag Varieties for Coxeter Groups

Part of: Special aspects of infinite or finite groups Representation theory of groups (Co)homology theory

Published online by Cambridge University Press:  09 January 2019

Pramod N. Achar ,
Simon Riche  and
Cristian Vay
Pramod N. Achar
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA Email: pramod@math.lsu.edu
Simon Riche
Affiliation:
Université Clermont Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand, France Email: simon.riche@uca.fr
Cristian Vay
Affiliation:
Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, CIEM–CONICET, Córdoba, Argentina Email: vay@famaf.unc.edu.ar
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Abstract

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.

Keywords

perverse sheafflag varietyCoxeter group

MSC classification

Primary: 14F05: Sheaves, derived categories of sheaves and related constructions
Secondary: 20C08: Hecke algebras and their representations 20F55: Reflection and Coxeter groups
Type
Article
Information
Canadian Journal of Mathematics , Volume 72 , Issue 1 , February 2020 , pp. 1 - 55
Copyright
© Canadian Mathematical Society 2018 

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Footnotes

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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