Appendix: Gelfand pairs associated with the action of G

We show that the action of the group G on each level of the rooted binary tree T2 is 2-point homogeneous, giving rise to symmetric Gelfand pairs. The corresponding decomposition into irreducible G-submodules and the associated spherical functions are described.

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Bibliographic Details
Published in:European journal of combinatorics 2012-10, Vol.33 (7), p.1422-1426
Main Authors: D’Angeli, Daniele, Donno, Alfredo
Format: Article
Language:English
Subjects:
Combinatorial analysis
Decomposition
Group theory
Trees
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Description
Summary:We show that the action of the group G on each level of the rooted binary tree T2 is 2-point homogeneous, giving rise to symmetric Gelfand pairs. The corresponding decomposition into irreducible G-submodules and the associated spherical functions are described.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2012.03.007