Spherical representations of Lie supergroups

What is it about?

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 in type AIII|AIII, all spherical representations are self-dual.

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