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• W2621137149 abstract "Let $G$ be a connected, linear, real reductive Lie group with compact centre. Let $K<G$ be maximal compact. For a tempered representation $pi$ of $G$, we realise the restriction $pi|_K$ as the $K$-equivariant index of a Dirac operator on a homogeneous space of the form $G/H$, for a Cartan subgroup $H<G$. (The result in fact applies to every standard representation.) Such a space can be identified with a coadjoint orbit of $G$, so that we obtain an explicit version of Kirillov's orbit method for $pi|_K$. In a companion paper, we use this realisation of $pi|_K$ to give a geometric expression for the multiplicities of the $K$-types of $pi$, in the spirit of the quantisation commutes with reduction principle. This generalises work by Paradan for the discrete series to arbitrary tempered representations." @default.
• W2621137149 created "2017-06-09" @default.
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• W2621137149 date "2017-05-05" @default.
• W2621137149 modified "2023-09-23" @default.
• W2621137149 title "A geometric realisation of tempered representations restricted to maximal compact subgroups" @default.
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• W2621137149 doi "https://doi.org/10.48550/arxiv.1705.02088" @default.
• W2621137149 hasPublicationYear "2017" @default.
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