Let F,, r > 1, be a free group with r generators. In this paper, we study a principal series and a complementary series of irreducible unitary representations of F,, which are defined through the action of F, on its Poisson boundary, relative to a simple random walk. We show that the regular representation of F, can be written as a direct integral of the representations of the principal series and that the resulting harmonic analysis on the free group bears a close resemblance with the harmonic analysis of SL(2, IR).
Figa-Talamanca, A., Picardello, A.m. (1982). Spherical functions and harmonic analysis on free groups. JOURNAL OF FUNCTIONAL ANALYSIS, 47(3), 281-304 [10.1016/0022-1236(82)90108-2].
Spherical functions and harmonic analysis on free groups
Picardello A. M.
1982-01-01
Abstract
Let F,, r > 1, be a free group with r generators. In this paper, we study a principal series and a complementary series of irreducible unitary representations of F,, which are defined through the action of F, on its Poisson boundary, relative to a simple random walk. We show that the regular representation of F, can be written as a direct integral of the representations of the principal series and that the resulting harmonic analysis on the free group bears a close resemblance with the harmonic analysis of SL(2, IR).| File | Dimensione | Formato | |
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