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$$K$$-types of minimal representations ($$p$$-adic case). (English) Zbl 0856.22020
The Weil representation, originally invented to provide a representation-theoretic setting for the theory of theta series, is a minimal representation, meaning that it corresponds to coadjoint orbits of minimal dimension. This property turned out to yield a good generalization to other than metaplectic groups.
The present paper is concerned with $$p$$-adic groups of type $$D_n$$ or $$E_n$$. For these groups an explicit description of the $$K$$-types of the minimal representation is given, where $$K$$ is a hyperspecial maximal compact subgroup.

MSC:
 22E50 Representations of Lie and linear algebraic groups over local fields 22E35 Analysis on $$p$$-adic Lie groups 11F70 Representation-theoretic methods; automorphic representations over local and global fields