Free probability on <inline-formula><tex-math id="M1">\begin{document}$ C^{*}$\end{document}</tex-math></inline-formula>-algebras induced by hecke algebras over primes

Abstract

In this paper, we establish free-probabilistic models (H(Gp), ψp) on Hecke algebras H(Gp), and construct Hilbert-space representations of H (Gp), preserving free-probabilistic information from (H(Gp), ψp) , for primes p. From such free-probabilistic structures with representations, we study spectral properties of operators in C *-algebras generated by {H(Gp)} p:primes , via their free distributions.