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doi: 10.3934/dcdss.2019143
Free probability on $ C^{*}$-algebras induced by hecke algebras over primes
Ilwoo Cho 1,, and Palle Jorgense 2,
St. Ambrose Univ., Dept. of Math. & Stat., 421 Ambrose Hall, 518 W. Locust St., Davenport, IA 52803, USA
Univ. of Iowa, Dept. of Math., 14 McLean Hall, Iowa City, IA 52242, USA
* Corresponding author: Ilwoo Cho
Received August 2016 Revised March 2017 Published January 2019
In this paper, we establish free-probabilistic models $ \left( \mathcal{H}(G_{p}),\text{ }\psi _{p}\right)$ on Hecke algebras $ \mathcal{H}(G_{p})$, and construct Hilbert-space representations of $ \mathcal{H} (G_{p}),$ preserving free-probabilistic information from $ \left( \mathcal{H}(G_{p}),\text{ }\psi _{p}\right) ,$ for primes $ p.$ From such free-probabilistic structures with representations, we study spectral properties of operators in $ C^{*}$-algebras generated by $ \left\{ \mathcal{H}(G_{p})\right\}_{p:primes}$, via their free distributions.
Keywords: Free probability, free product, primes, Hecke algebras, representations.
Mathematics Subject Classification: Primary: 46L10, 46L53, 46L54, 47L55; Secondary: 05E15, 11G15, 11R47, 11R56.
Citation: Ilwoo Cho, Palle Jorgense. Free probability on $ C^{*}$-algebras induced by hecke algebras over primes. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2019143
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Ilwoo Cho Palle Jorgense
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