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.
Citation
Dennis Gaitsgory. David Kazhdan. "Algebraic groups over a 2-dimensional local field: Irreducibility of certain induced representations." J. Differential Geom. 70 (1) 113 - 128, May 2005. https://doi.org/10.4310/jdg/1143572015
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