Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589919 | Journal of Functional Analysis | 2015 | 51 Pages |
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)(G,K) of even type. Along the way, we compute the Harish-Chandra c -function of the symmetric superspace G/KG/K. By way of an application, we show that in type AIII|AIIIAIII|AIII, all spherical representations are self-dual.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Alexander Alldridge, Sebastian Schmittner,