Vol. 8, No. 1, 2014

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The Tannakian formalism and the Langlands conjectures

David Kazhdan, Michael Larsen and Yakov Varshavsky

Vol. 8 (2014), No. 1, 243–256
Abstract

Let H be a connected reductive group over an algebraically closed field of characteristic zero, and let Γ be an abstract group. In this note, we show that every homomorphism of Grothendieck semirings ϕ : K0+[H] K0+[Γ], which maps irreducible representations to irreducible, comes from a group homomorphism ρ : Γ H(K). We also connect this result with the Langlands conjectures.

Keywords
Tannaka duality, Langlands conjectures
Mathematical Subject Classification 2010
Primary: 11R39
Secondary: 11F80, 17B10, 18D10
Milestones
Received: 2 September 2012
Revised: 20 August 2013
Accepted: 19 September 2013
Published: 20 April 2014
Authors
David Kazhdan
Einstein Institute of Mathematics
Hebrew University
Givat Ram
91904 Jerusalem
Israel
Michael Larsen
Department of Mathematics
Indiana University
Rawles Hall
Bloomington, IN 47405-5701
United States
Yakov Varshavsky
Einstein Institute of Mathematics
Hebrew University
Givat Ram
91904 Jerusalem
Israel