## Journal of Differential Geometry

### Algebraic groups over a 2-dimensional local field: Irreducibility of certain induced representations

#### Abstract

Let G be a split reductive group over a local field K, and let G((t)) be the corresponding loop group. In [1], we have introduced the notion of a representation of (the group of K-points) of G((t)) on a pro-vector space. In addition, we have defined an induction procedure, which produced G((t))-representations from usual smooth representations of G. We have conjectured that the induction of a cuspidal irreducible representation of G is irreducible. In this paper, we prove this conjecture for G=SL2.

#### Article information

Source
J. Differential Geom., Volume 70, Number 1 (2005), 113-128.

Dates
First available in Project Euclid: 28 March 2006

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1143572015

Digital Object Identifier
doi:10.4310/jdg/1143572015

Mathematical Reviews number (MathSciNet)
MR2192062

Zentralblatt MATH identifier
1094.22002

#### Citation

Gaitsgory, Dennis; Kazhdan, David. Algebraic groups over a 2-dimensional local field: Irreducibility of certain induced representations. J. Differential Geom. 70 (2005), no. 1, 113--128. doi:10.4310/jdg/1143572015. https://projecteuclid.org/euclid.jdg/1143572015