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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
DOI: https://doi.org/10.1090/S1088-4165-06-00290-1
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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Additional Information

Immanuel Halupczok
Affiliation: Albert-Ludwigs-Universität Freiburg, Mathematisches Institut, Eckerstraße 1, 79104 Freiburg, Germany
Email: math@karimmi.de

DOI: https://doi.org/10.1090/S1088-4165-06-00290-1
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

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