Unipotent Representations and Microlocalization
Abstract
We develop a theory of microlocalization for Harish-Chandra modules, adapting a construction of Losev (Losev2011). We explore the applications of this theory to unipotent representations of real reductive groups. For complex groups, we deduce a formula for the K-multiplicities of unipotent representations attached to a nilpotent orbit , proving an old conjecture of Vogan (Vogan1991) in a large family of cases.
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