Spherical representations of Lie supergroups
Representation Theory
2016-06-21 v2 Mathematical Physics
math.MP
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 of even type. Along the way, we compute the Harish-Chandra -function of the symmetric superspace . By way of an application, we show that all spherical representations are self-dual in type AIII|AIII.
Cite
@article{arxiv.1303.6815,
title = {Spherical representations of Lie supergroups},
author = {Alexander Alldridge and Sebastian Schmittner},
journal= {arXiv preprint arXiv:1303.6815},
year = {2016}
}
Comments
37 pages; title changed; substantially revised version; accepted for publication, J. Func. Anal. (2014)