Book chapter
Free Products of C-Probability Spaces from p-Adic Hecke Algebras
Advances in Complex Analysis and Operator Theory, pp.55-99
Trends in Mathematics, Springer International Publishing
09/27/2017
DOI: 10.1007/978-3-319-62362-7_4
Abstract
In this paper, by establishing suitable free-probabilistic models on the Hecke algebras \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\mathcal{H}(G_p)$$
\end{document}, we study (i) free probability on \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\mathcal{H}(G_p)$$
\end{document}, (ii) Hilbert-space representations of \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\mathcal{H}(G_p)$$
\end{document}, (iii) the C*-algebras \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\mathbb{H}(G_p)$$
\end{document} induced by \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\mathcal{H}(G_p)$$
\end{document}, and (iv) free probability on the free product C*-probability space \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\mathbb{H}_p\;\mathrm{of}\;\mathbb{H}(G_p)$$
\end{document}’s over primes p, where Gp are the general linear groups \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$GL_2(\mathbb{Q}_p)$$
\end{document} over the p-adic number fields \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\mathbb{Q}_p$$
\end{document}, for primes p. In particular, we are mainly interested in the operator-algebraic properties the free product C* -probability space \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\mathbb{H}_p$$
\end{document}, and operator-theoretic informations of the elements of \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\mathbb{H}_p$$
\end{document} in terms of their free-distributional data. As an application of the main results, an embedded free-probabilistic sub-structure generated by projections of \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$\mathbb{H}_p$$
\end{document}is considered in detail.
Details
- Title: Subtitle
- Free Products of C-Probability Spaces from p-Adic Hecke Algebras
- Creators
- Il Woo Cho - Saint Ambrose UniversityPalle E. T Jorgensen - University of Iowa
- Resource Type
- Book chapter
- Publication Details
- Advances in Complex Analysis and Operator Theory, pp.55-99
- Publisher
- Springer International Publishing; Cham
- Series
- Trends in Mathematics
- DOI
- 10.1007/978-3-319-62362-7_4
- eISSN
- 2297-024X
- ISSN
- 2297-0215
- Language
- English
- Date published
- 09/27/2017
- Academic Unit
- Mathematics
- Record Identifier
- 9984240771302771
Metrics
16 Record Views