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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
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