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arXiv · 1303.6815

Spherical representations of Lie supergroups

Alexander Alldridge·Sebastian Schmittner
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Abstract

The classical Cartan-Helgason theorem characterises finite-dimensional spherical representations of reductive Lie groups in terms of their highest weights. We generalise the theorem to the case of a reductive symmetric supergroup pair $(G,K)$ of even type. Along the way, we compute the Harish-Chandra $c$-function of the symmetric superspace $G/K$. By way of an application, we show that all spherical representations are self-dual in type AIII|AIII.

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BibTeXRIS

Alexander Alldridge, Sebastian Schmittner. 2013-03-27. Spherical representations of Lie supergroups. https://doi.org/10.1016/j.jfa.2014.11.018

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