• DOI:10.46298/epiga.2019.volume3.4353
• Corpus ID: 119606495

Equivariant perverse sheaves on Coxeter arrangements and buildings

@article{Weissman2019EquivariantPS,
  title={Equivariant perverse sheaves on Coxeter arrangements and buildings},
  author={Martin H. Weissman},
  journal={{\'E}pijournal de G{\'e}om{\'e}trie Alg{\'e}brique},
  year={2019}
}

• M. Weissman
• Published 23 June 2017
• Mathematics
• Épijournal de Géométrie Algébrique

When $W$ is a finite Coxeter group acting by its reflection representation on
$E$, we describe the category ${\mathsf{Perv}}_W(E_{\mathbb C},
{\mathcal{H}}_{\mathbb C})$ of $W$-equivariant perverse sheaves on $E_{\mathbb
C}$, smooth with respect to the stratification by reflection hyperplanes. By
using Kapranov and Schechtman's recent analysis of perverse sheaves on
hyperplane arrangements, we find an equivalence of categories from
${\mathsf{Perv}}_W(E_{\mathbb C}, {\mathcal{H}}_{\mathbb C})$ to a category of
finite-dimensional modules over an algebra given by explicit generators and
relations.
We also define categories of equivariant perverse sheaves on affine
buildings, e.g., $G$-equivariant perverse sheaves on the Bruhat--Tits building
of a $p$-adic group $G$. In this setting, we find that a construction of
Schneider and Stuhler gives equivariant perverse sheaves associated to depth
zero representations.

Comment: 28 pages, 6 figures. v5 processed for publication in Epiga