We present a new construction of finite Gelfand pairs by looking at the action of the full automorphism group of a finite spherically homogeneous rooted tree of type r on the variety V(r, s) of all spherically homogeneous subtrees of type s. This generalizes well-known examples as the finite ultrametric space, the Hamming scheme and the Johnson scheme. We also present further generalizations of these classical examples. The first two are based on Harary's notions of composition and exponentiation of group actions. Finally, the generalized Johnson scheme provides the inductive step for the harmonic analysis of our main construction. (C) 2005 Elsevier Inc. All fights reserved.

Trees, wreath products and finite Gelfand pairs / Scarabotti, Fabio; Tullio Ceccherini, Silberstein; Filippo, Tolli. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 206:2(2006), pp. 503-537. [10.1016/j.aim.2005.10.002]

Trees, wreath products and finite Gelfand pairs

SCARABOTTI, Fabio;
2006

Abstract

We present a new construction of finite Gelfand pairs by looking at the action of the full automorphism group of a finite spherically homogeneous rooted tree of type r on the variety V(r, s) of all spherically homogeneous subtrees of type s. This generalizes well-known examples as the finite ultrametric space, the Hamming scheme and the Johnson scheme. We also present further generalizations of these classical examples. The first two are based on Harary's notions of composition and exponentiation of group actions. Finally, the generalized Johnson scheme provides the inductive step for the harmonic analysis of our main construction. (C) 2005 Elsevier Inc. All fights reserved.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/71456
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