The spherical principal series of a non-commutative free group may be analytically continued to yield a series of uniformly bounded representations, much as the spherical representations π_{(1/2)+ it} of SL(2, R) may be analytically continued in the strip 0 < Re z < 1. This series of uniformly bounded representations was constructed and studied by A. M. MANTERO and A. ZAPPA. Independently T. PYTLIK and R. SZWARC introduced and studied representations of the free group which contain a series of subrepresentations indexed by spherical functions. Both series consist of irreducible representations and include the spherical complementary series. The aim of this paper is to prove that the non-unitary uniformly bounded representations of the two series are also equivalent.
Equivalence of two series of spherical representations of a free group
MANTERO, ANNA MARIA;ZAPPA, ANNA
1993-01-01
Abstract
The spherical principal series of a non-commutative free group may be analytically continued to yield a series of uniformly bounded representations, much as the spherical representations π_{(1/2)+ it} of SL(2, R) may be analytically continued in the strip 0 < Re z < 1. This series of uniformly bounded representations was constructed and studied by A. M. MANTERO and A. ZAPPA. Independently T. PYTLIK and R. SZWARC introduced and studied representations of the free group which contain a series of subrepresentations indexed by spherical functions. Both series consist of irreducible representations and include the spherical complementary series. The aim of this paper is to prove that the non-unitary uniformly bounded representations of the two series are also equivalent.
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