Kerov, Serguei; Olshanski, Grigori; Vershik, Anatoli Harmonic analysis on the infinite symmetric group. A deformation of the regular representation. (English. Abridged French version) Zbl 0796.43005 C. R. Acad. Sci., Paris, Sér. I 316, No. 8, 773-778 (1993). Let \(S(n)\) be the symmetric group of \(\{1,2,\dots,n\}\) and \(S = \bigcup S(n)\) the group of finite permutations of \(\{1,2,\dots\}\). The authors construct a family of unitary representations \(T_ z\) of \(S\), parametrized by complex numbers \(z\). These representations can be viewed as deformations of the regular \(T_ \infty\) of \(S\). They exhibit direct integral decompositions of these representations. Reviewer: D.Miličić (Salt Lake City) Cited in 5 ReviewsCited in 44 Documents MSC: 43A65 Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) 20C32 Representations of infinite symmetric groups Keywords:symmetric group; group of finite permutations; unitary representations; deformations; integral decompositions PDFBibTeX XMLCite \textit{S. Kerov} et al., C. R. Acad. Sci., Paris, Sér. I 316, No. 8, 773--778 (1993; Zbl 0796.43005)