Open AccessCategorical Langlands correspondence for 𝑆𝑂_{𝑛,1}(ℝ)
Author(s) -
Immanuel Halupczok
Publication year - 2006
Publication title -
representation theory
Language(s) - English
Resource type - Journals
ISSN - 1088-4165
DOI - 10.1090/s1088-4165-06-00290-1
Subject(s) - langlands dual group , bijection , mathematics , conjecture , equivariant map , langlands program , space (punctuation) , equivalence (formal languages) , pure mathematics , variety (cybernetics) , context (archaeology) , combinatorics , algebra over a field , linguistics , geography , statistics , philosophy , archaeology
In the context of the local Langlands philosopy for R \mathbb {R} , Adams, Barbasch and Vogan describe a bijection between the simple Harish-Chandra modules for a real reductive group G ( R ) 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 ( R ) 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 ( R ) G(\mathbb {R}) is a generalized Lorentz group SO n , 1 ( R ) \operatorname {SO}_{n,1}(\mathbb {R}) .