Spherical functions and uniformly bounded representations of free groups

Tadeusz Pytlik

Studia Mathematica (1991)

  • Volume: 100, Issue: 3, page 237-250
  • ISSN: 0039-3223

Abstract

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We give a construction of an analytic series of uniformly bounded representations of a free group G, through the action of G on its Poisson boundary. These representations are irreducible and give as their coefficients all the spherical functions on G which tend to zero at infinity. The principal and the complementary series of unitary representations are included. We also prove that this construction and the other known constructions lead to equivalent representations.

How to cite

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Pytlik, Tadeusz. "Spherical functions and uniformly bounded representations of free groups." Studia Mathematica 100.3 (1991): 237-250. <http://eudml.org/doc/215886>.

@article{Pytlik1991,
abstract = {We give a construction of an analytic series of uniformly bounded representations of a free group G, through the action of G on its Poisson boundary. These representations are irreducible and give as their coefficients all the spherical functions on G which tend to zero at infinity. The principal and the complementary series of unitary representations are included. We also prove that this construction and the other known constructions lead to equivalent representations.},
author = {Pytlik, Tadeusz},
journal = {Studia Mathematica},
keywords = {free group; uniformly bounded representation; spherical functions; analytic series of representations; unitary representations},
language = {eng},
number = {3},
pages = {237-250},
title = {Spherical functions and uniformly bounded representations of free groups},
url = {http://eudml.org/doc/215886},
volume = {100},
year = {1991},
}

TY - JOUR
AU - Pytlik, Tadeusz
TI - Spherical functions and uniformly bounded representations of free groups
JO - Studia Mathematica
PY - 1991
VL - 100
IS - 3
SP - 237
EP - 250
AB - We give a construction of an analytic series of uniformly bounded representations of a free group G, through the action of G on its Poisson boundary. These representations are irreducible and give as their coefficients all the spherical functions on G which tend to zero at infinity. The principal and the complementary series of unitary representations are included. We also prove that this construction and the other known constructions lead to equivalent representations.
LA - eng
KW - free group; uniformly bounded representation; spherical functions; analytic series of representations; unitary representations
UR - http://eudml.org/doc/215886
ER -

References

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  10. [10] T. Pytlik, Spherical functions and uniformly bounded representations of free groups, preprint 60 (1986), Math. Inst. Univ. Wrocław. Zbl0754.22002
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