# Canonical and Boundary Representations on a Hyperboloid of One Sheet

Research paper by V. F. Molchanov

Indexed on: 01 Mar '04Published on: 01 Mar '04Published in: Acta applicandae mathematicae

#### Abstract

For the hyperboloid of one sheet X=G/H, G=SO0(1,2), H=SO0(1,1), canonical representations Rλ,ν, λ∈C, ν=0,1, are defined as the restrictions to G of representations of the overgroup $$\tilde G$$=SO0(2,2) associated with a cone. They act on the torus containing two copies of X as open G-orbits. We study boundary representations generated by Rλ,ν. For some λ, they contain Jordan blocks. The decomposition of Rλ,ν into irreducible constituents includes a finite number (depending on λ) of irreducible parts of the boundary representations.