Thursday, March 28, 2013

1303.6815 (Alexander Alldridge et al.)

Cartan-Helgason for supergroups    [PDF]

Alexander Alldridge, Sebastian Schmittner
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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