Trees, wreath products and finite Gelfand pairs |
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Authors: | Tullio Ceccherini-Silberstein Fabio Scarabotti |
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Institution: | a Dipartimento di Ingegneria, Università del Sannio, C.so Garibaldi 107, 82100 Benevento, Italy b Dipartimento MeMoMat, Università degli Studi di Roma “La Sapienza”, via A. Scarpa 8, 00161 Roma, Italy c Dipartimento di Matematica, Università di Roma Tre, L.go S. Leonardo Murialdo 1, 00146 Roma, Italy |
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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. |
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Keywords: | 43A90 20B25 20E08 20E22 22D15 33C80 43A85 |
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