Equivariant perverse sheaves on Coxeter arrangements and buildings

  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},
  • 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… 

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