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- W5414097 abstract "For the group O(p;q) we give a new construction of its minimal unitary represen- tation via Euclidean Fourier analysis. This is an extension of the q = 2 case, where the representation is the mass zero, spin zero representation realized in a Hilbert space of solutions to the wave equation. The group O(p;q) acts as the Mobius group of conformal transformations on R p 1;q 1 , and preserves a space of solutions of the ultrahyperbolic Laplace equation on R p 1;q 1 . We construct in an intrinsic and natural way a Hilbert space of solutions so that O(p;q) becomes a continuous irreducible unitary representation in this Hilbert space. We also prove that this rep- resentation is unitarily equivalent to the representation on L 2 (C), where C is the conical subvariety of the nilradical of a maximal parabolic subalgebra obtained by intersecting with the minimal nilpotent orbit in the Lie algebra of O(p;q)." @default.
- W5414097 created "2016-06-24" @default.
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- W5414097 date "2002-01-01" @default.
- W5414097 modified "2023-09-27" @default.
- W5414097 title "Analysis on the minimal representation of" @default.
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