Opuscula Math. 36, no. 3 (2016), 337-373
http://dx.doi.org/10.7494/OpMath.2016.36.3.337
Opuscula Mathematica
Certain group dynamical systems induced by Hecke algebras
Abstract. In this paper, we study dynamical systems induced by a certain group \(\mathfrak{T}_{N}^{K}\) embedded in the Hecke algebra \(\mathcal{H}(G_{p})\) induced by the generalized linear group \(G_{p} = GL_{2}(\mathbb{Q}_{p})\) over the \(p\)-adic number fields \(\mathbb{Q}_{p}\) for a fixed prime \(p\). We study fundamental properties of such dynamical systems and the corresponding crossed product algebras in terms of free probability on the Hecke algebra \(\mathcal{H}(G_{p})\).
Keywords: free probability, free moments, free cumulants, Hecke algebra, normal Hecke subalgebra, free probability spaces, representations, operators, Hilbert spaces, dynamical systems, crossed product algebras.
Mathematics Subject Classification: 05E15, 11R47, 46L10, 47L30, 47L55.
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- Ilwoo Cho
- St. Ambrose University, Department of Mathematics and Statistics, 421 Ambrose Hall, 518 W. Locust St., Davenport, Iowa, 52803, USA
- Communicated by P.A. Cojuhari.
- Received: 2015-03-30.
- Revised: 2015-05-19.
- Accepted: 2015-07-06.
- Published online: 2016-02-21.
