Algebraic groups over a 2-dimensional local field: Irreducibility of certain induced representations
Gaitsgory, Dennis ; Kazhdan, David
J. Differential Geom., Tome 69 (2005) no. 3, p. 113-128 / Harvested from Project Euclid
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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.
Publié le : 2005-05-14
Classification:  
@article{1143572015,
     author = {Gaitsgory, Dennis and Kazhdan, David},
     title = {Algebraic groups over a 2-dimensional local field: Irreducibility of certain induced representations},
     journal = {J. Differential Geom.},
     volume = {69},
     number = {3},
     year = {2005},
     pages = { 113-128},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1143572015}
}

Gaitsgory, Dennis; Kazhdan, David. Algebraic groups over a 2-dimensional local field: Irreducibility of certain induced representations. J. Differential Geom., Tome 69 (2005) no. 3, pp.  113-128. http://gdmltest.u-ga.fr/item/1143572015/