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Explicit Hilbert spaces for certain unipotent representations II

Alexander Dvorsky·Siddhartha Sahi
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Abstract

We construct an explicit realization of a minimal representation of G, where G is the conformal group of a real Jordan algebra N. We characterize spherical vectors for these representation and prove that they are closely related to the Bessel K-function $K_τ(z)$. The resulting construction can be used to study tensor powers of the minimal representation and establish an extension of the Howe duality correspondence to some exceptional groups.

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BibTeXRIS

Alexander Dvorsky, Siddhartha Sahi. 1999-04-13. Explicit Hilbert spaces for certain unipotent representations II. https://doi.org/10.1007/s002220050347

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