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.

CECCHERINI SILBERSTEIN, T., Scarabotti, F., Tolli, F. (2006). Trees, wreath products and finite Gelfand pairs. ADVANCES IN MATHEMATICS, 206, 503-537.

Trees, wreath products and finite Gelfand pairs

TOLLI, FILIPPO
2006-01-01

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.
2006
CECCHERINI SILBERSTEIN, T., Scarabotti, F., Tolli, F. (2006). Trees, wreath products and finite Gelfand pairs. ADVANCES IN MATHEMATICS, 206, 503-537.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/124070
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