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Sous-groupes paraboliques et représentations de groupes branchés

Contributors

Bartholdi, Laurent; Grigorchuk, Rostislav

Published in

Comptes rendus de l'Académie des sciences. Série 1, Mathématique, vol. 332, no. 9, p. 789-794

Publication date

2001

Abstract

Let G be a branch group (as defined by Grigorchuk) acting on a tree T. A parabolic subgroup P is the stabiliser of an infinite geodesic ray in T. We denote by $ ho_{G/P}$ the associated quasi-regular representation. If G is discrete, these representations are irreducible, but if G is profinite, they split as a direct sum of finite-dimensionalrepresentations $ ho_{G/P_{n+1}}ominus ho_{G/P_n}$, where P_n is the stabiliser of a level-n vertex in T. For a few concrete examples, we completely split $ ho_{G/P_n}$ in irreducible components. $(G,P_n)$ and $(G,P)$ are Gelfand pairs, whence new occurrences of abelian Hecke algebra.

Classification

  • arxiv : math.GR

UNIGE affiliation entities

Citation (ISO format)

BARTHOLDI, Laurent, GRIGORCHUK, Rostislav. Sous-groupes paraboliques et représentations de groupes branchés. In: Comptes rendus de l’Académie des sciences. Série 1, Mathématique, 2001, vol. 332, n° 9, p. 789–794. doi: 10.1016/S0764-4442(01)01946-2

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Journal ISSN

0764-4442
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Technical informations

Creation

08/11/2010 11:28:00

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08/11/2010 11:28:00

Update

14/03/2023 16:08:28

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14/03/2023 16:08:28

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