#### 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 $\Gamma$ be an abstract group. In this note, we show that every homomorphism of Grothendieck semirings $\varphi :{K}_{0}^{+}\left[H\right]\to {K}_{0}^{+}\left[\Gamma \right]$, which maps irreducible representations to irreducible, comes from a group homomorphism $\rho :\Gamma \to H\left(K\right)$. 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
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