A sufficient condition for the complete reducibility of the regular representation
1979; Elsevier BV; Volume: 34; Issue: 2 Linguagem: Inglês
10.1016/0022-1236(79)90033-8
ISSN1096-0783
AutoresLarry Baggett, Keith F. Taylor,
Tópico(s)Advanced Algebra and Geometry
ResumoThe “Mackey machine” is heavily employed to prove the following theorem. Let G be a separable locally compact group. Suppose that every positive definite function p on G which vanishes at infinity is associated with the regular representation R, i.e., p(g) = (Rgϑ, ϑ) for some L2 function ϑ. Then R decomposes into a direct sum of irreducible representations. This generalizes the theorem of Figà-Talamanca for unimodular groups. Although we use his result several times, our techniques are basically very different, the most difficult part occurring in a connected Lie group context.
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