On the de Sitter spectra

Abstract

The principal series of the unitary irreducible representations of the noncompact symplectic groupSp 1,1 are constructed using a generalization to the quaternionic field of Grave’s paper onU p,q . The spectra of these representations are explicitly calculated. SinceSp 1,1 is the covering of the de Sitter groupO 4,1, its invariants are related by contraction to those of the Poincaré group.