Twisted geometric Satake equivalence

Michael Finkelberg, Sergey Lysenko

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

Let k be an algebraically closed field and O = k[[t]] F = k((t)). For an almost simple algebraic group G we classify central extensions 1 →G m→ E →G (F) 1; any such extension splits canonically over G(O). Fix a positive integer N and a primitive character : N(K) ℚell;* (under some assumption on the characteristic of k). Consider the category of G(O)-bi-invariant perverse sheaves on E with Gm-monodromy . We show that this is a tensor category, which is tensor equivalent to the category of representations of a reductive group E,N. We compute the root datum of E,N.

Original languageEnglish
Pages (from-to)719-739
Number of pages21
JournalJournal of the Institute of Mathematics of Jussieu
Volume9
Issue number4
DOIs
Publication statusPublished - Oct 2010
Externally publishedYes

Keywords

  • geometric Langlands program
  • monodromic perverse sheaves
  • Satake isomorphism

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