Mixed Perverse Sheaves on Flag Varieties for Coxeter Groups
Canadian journal of mathematics, Tome 72 (2020) no. 1, pp. 1-55
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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.
Achar, Pramod N.; Riche, Simon; Vay, Cristian. Mixed Perverse Sheaves on Flag Varieties for Coxeter Groups. Canadian journal of mathematics, Tome 72 (2020) no. 1, pp. 1-55. doi: 10.4153/CJM-2018-034-0
@article{10_4153_CJM_2018_034_0,
author = {Achar, Pramod N. and Riche, Simon and Vay, Cristian},
title = {Mixed {Perverse} {Sheaves} on {Flag} {Varieties} for {Coxeter} {Groups}},
journal = {Canadian journal of mathematics},
pages = {1--55},
year = {2020},
volume = {72},
number = {1},
doi = {10.4153/CJM-2018-034-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2018-034-0/}
}
TY - JOUR AU - Achar, Pramod N. AU - Riche, Simon AU - Vay, Cristian TI - Mixed Perverse Sheaves on Flag Varieties for Coxeter Groups JO - Canadian journal of mathematics PY - 2020 SP - 1 EP - 55 VL - 72 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2018-034-0/ DO - 10.4153/CJM-2018-034-0 ID - 10_4153_CJM_2018_034_0 ER -
%0 Journal Article %A Achar, Pramod N. %A Riche, Simon %A Vay, Cristian %T Mixed Perverse Sheaves on Flag Varieties for Coxeter Groups %J Canadian journal of mathematics %D 2020 %P 1-55 %V 72 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2018-034-0/ %R 10.4153/CJM-2018-034-0 %F 10_4153_CJM_2018_034_0
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