Free probability on Hecke algebras

DOI10.1007/S11785-014-0403-1zbMath1325.11127OpenAlexW2045166840MaRDI QIDQ746787

Ilwoo Cho, Timothy L. Gillespie

Publication date: 20 October 2015

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-014-0403-1

zbMATH Keywords

Hecke algebrasfree probabilityfree cumulantsfree momentsfree probability spaces\(p\)-adic number fieldsnormal Hecke subalgebras

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) General theory of von Neumann algebras (46L10) Noncommutative probability and statistics (46L53) Operator theory over fields other than (mathbb{R}), (mathbb{C}) or the quaternions; non-Archimedean operator theory (47S10) Representations of (nonselfadjoint) operator algebras (47L55) Automorphisms of selfadjoint operator algebras (46L40)

Related Items (11)

Adelic analysis and functional analysis on the finite Adele ring ⋮ Deformation of semicircular and circular laws via p-adic number fields and sampling of primes ⋮ Free Products of C*-Probability Spaces from p-Adic Hecke Algebras ⋮ Factorization of \(\mathbb C\)-valued functions induced by graphs ⋮ Free probability on \(W^{*}\)-dynamical systems determined by \(GL_{2}(\mathbb {Q} _{p})\): generalized Hecke algebras ⋮ Free semicircular families in free product Banach \(\ast\)-algebras induced by \(p\)-adic number fields over primes \(p\) ⋮ Semicircular elements induced by p-adic number fields ⋮ Certain group dynamical systems induced by Hecke algebras ⋮ Analysis of free products of the general linear groups 𝐺𝐿₂(ℚ_{𝕡}) and Hecke algebras ℋ(𝒢ℒ₂(ℚ_{𝕡})) over primes 𝕡 ⋮ Free probability on \( C^*\)-algebras induced by Hecke algebras over primes ⋮ Circular-Like and Circular Elements in Free Product Banach $${*}$$ ∗ -Algebras Induced by p-Adic Number Fields $$\mathbb {Q}_{p}$$ Q p Over Primes p

Cites Work

• Unnamed Item
• Operators induced by prime numbers
• Krein-space representations of arithmetic functions determined by primes
• Prime number theorems for Rankin-Selberg \(L\)-functions over number fields
• Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index
• Krein-Space Operators Induced by Dirichlet Characters
• Free Random Variables
• Combinatorial theory of the free product with amalgamation and operator-valued free probability theory
• CLASSIFICATION ON ARITHMETIC FUNCTIONS AND CORRESPONDING FREE-MOMENT L-FUNCTIONS
• p-adic Banach space operators and adelic Banach space operators

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