Trees, wreath products and finite Gelfand pairs

DOI10.1016/j.aim.2005.10.002zbMath1106.43006OpenAlexW2004325974MaRDI QIDQ850014

Filippo Tolli, Fabio Scarabotti, Tullio G. Ceccherini Silberstein

Publication date: 15 November 2006

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2005.10.002

zbMATH Keywords

wreath productsrooted treesJohnson schemeHamming schemefinite ultrametric spacefinite Gelfand pairs

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Harmonic analysis on homogeneous spaces (43A85) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Extensions, wreath products, and other compositions of groups (20E22) Harmonic analysis and spherical functions (43A90) Groups acting on trees (20E08) Group algebras of locally compact groups (22D15)

Related Items (20)

Spectral analysis of finite Markov chains with spherical symmetries ⋮ A group of automorphisms of the rooted dyadic tree and associated Gelfand pairs ⋮ Induced representations and harmonic analysis on finite groups ⋮ The Okounkov-Vershik approach to the representation theory of \(G\sim S_n\) ⋮ Induced representations and Mackey theory. ⋮ Clifford theory and applications. ⋮ Representation theory of wreath products of finite groups ⋮ Zonal polynomials for wreath products ⋮ Gelfand pairs associated with the action of graph automaton groups ⋮ The lumpability property for a family of Markov chains on poset block structures ⋮ Harmonic analysis of finite lamplighter random walks ⋮ On exponentiation, p-automata and HNN extensions of free abelian groups ⋮ Finite Gelfand pairs and cracking points of the symmetric groups ⋮ Wreath product generalizations of the triple \((S_{2n},H_n,\varphi)\) and their spherical functions. ⋮ From parking functions to Gelfand pairs ⋮ A family of finite Gelfand pairs associated with wreath products ⋮ Wreath product action on generalized Boolean algebras ⋮ Harmonic analysis on a finite homogeneous space II: The Gelfand–Tsetlin decomposition ⋮ Crested products of Markov chains ⋮ Mackey's theory of \(\tau\)-conjugate representations for finite groups.

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