Explicit Hilbert spaces for certain unipotent representations

  title={Explicit Hilbert spaces for certain unipotent representations},
  author={Siddhartha Sahi},
Let G be the universal cover of the group of automorphisms of a symmetric tube domain and let P = L N 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… CONTINUE READING
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