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arXiv · 1805.12038

Unipotent Representations and Microlocalization

Lucas Mason-Brown
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Abstract

We develop a theory of microlocalization for Harish-Chandra modules, adapting a construction of Losev (\cite{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 $\OO$, proving an old conjecture of Vogan (\cite{Vogan1991}) in a large family of cases.

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Lucas Mason-Brown. 2018-05-30. Unipotent Representations and Microlocalization. https://arxiv.org/abs/1805.12038

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