Opuscula Mathematica
Opuscula Math. 36, no. 2 (), 153-187
http://dx.doi.org/10.7494/OpMath.2016.36.2.153
Opuscula Mathematica

Free probability on Hecke algebras and certain group C*-algebras induced by Hecke algebras


Abstract. In this paper, by establishing free-probabilistic models on the Hecke algebras \(\mathcal{H}\left(GL_{2}(\mathbb{Q}_{p})\right)\) induced by \(p\)-adic number fields \(\mathbb{Q}_{p}\), we construct free probability spaces for all primes \(p\). Hilbert-space representations are induced by such free-probabilistic structures. We study \(C^{*}\)-algebras induced by certain partial isometries realized under the representations.
Keywords: free probability, free moments, free cumulants, Hecke algebras, normal Hecke subalgebras, representations, groups, group \(C^{*}\)-algebras.
Mathematics Subject Classification: 05E15, 11R47, 46L54, 47L15, 47L55.
Cite this article as:
Ilwoo Cho, Free probability on Hecke algebras and certain group C*-algebras induced by Hecke algebras, Opuscula Math. 36, no. 2 (2016), 153-187, http://dx.doi.org/10.7494/OpMath.2016.36.2.153
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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