The Tannakian formalism and the Langlands conjectures

Kazhdan, David; Larsen, Michael; Varshavsky, Yakov

doi:10.2140/ant.2014.8.243

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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

DOI: 10.2140/ant.2014.8.243

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 $ϕ : K_{0}^{+} [H] \to K_{0}^{+} [Γ]$ , which maps irreducible representations to irreducible, comes from a group homomorphism $ρ : Γ \to H (K)$ . 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

Vol. 8, No. 1, 2014