Explicit Hilbert spaces for certain unipotent representations

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Abstract

Let G be the universal cover of the group of automorphisms of a symmetric tube domain and let P=LN be its Shilov boundary parabolic subgroup. This paper attaches an irreducible unitary representation of G to each of the (finitely many)L-orbits on n*. The Hilbert space of the representation consists of functions on the orbit which are square-integrable with respect to a certain L-equivariant measure. The representation remains irreducible when restricted to P, and descends to a quotient of G which is, at worst, the double cover of a linear group. If the L-orbit is not open (in n*), the construction gives a unipotent representation of G.

Original languageEnglish (US)
Pages (from-to)409-418
Number of pages10
JournalInventiones Mathematicae
Volume110
Issue number1
DOIs
StatePublished - Dec 1992
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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