Free Probability on Hecke Algebras

In this paper, we establish a free-probabilistic model on the Hecke algebras induced by p -adic number fields. It provides a new bridge between operator algebra theory and number theory. Based on number-theoretic and algebraic results from Hecke algebra theory, we consider operator-theoretic structu...

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Bibliographic Details
Published in:Complex analysis and operator theory 2015-10, Vol.9 (7), p.1491-1531
Main Authors: Cho, Ilwoo, Gillespie, Timothy L.
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
Operator Theory
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Summary:In this paper, we establish a free-probabilistic model on the Hecke algebras induced by p -adic number fields. It provides a new bridge between operator algebra theory and number theory. Based on number-theoretic and algebraic results from Hecke algebra theory, we consider operator-theoretic structures and properties via our free-probabilistic model.
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-014-0403-1