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Categorical Langlands correspondence for $\operatorname {SO}_{n,1}(\mathbb {R})$

Author: Immanuel Halupczok
Journal: Represent. Theory 10 (2006), 223-253
MSC (2000): Primary 22E50, 20G05, 32S60; Secondary 11S37
Published electronically: April 6, 2006
MathSciNet review: 2219113
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Abstract: In the context of the local Langlands philosopy for $\mathbb {R}$, Adams, Barbasch and Vogan describe a bijection between the simple Harish-Chandra modules for a real reductive group $G(\mathbb {R})$ and the space of “complete geometric parameters”—a space of equivariant local systems on a variety on which the Langlands-dual of $G(\mathbb {R})$ acts. By a conjecture of Soergel, this bijection can be enhanced to an equivalence of categories. In this article, that conjecture is proven in the case where $G(\mathbb {R})$ is a generalized Lorentz group $\operatorname {SO}_{n,1}(\mathbb {R})$.

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Immanuel Halupczok
Affiliation: Albert-Ludwigs-Universität Freiburg, Mathematisches Institut, Eckerstraße 1, 79104 Freiburg, Germany

Received by editor(s): June 5, 2005
Received by editor(s) in revised form: February 6, 2006
Published electronically: April 6, 2006
Additional Notes: The author was supported in part by the “Landesgraduiertenförderung Baden-Württemberg”. He also wishes to thank Wolfgang Soergel for making this article possible
Article copyright: © Copyright 2006 Immanuel Halupczok