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Free Probability on Hecke Algebras

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, 421 Ambrose Hall, Saint Ambrose University, 518 W. Locust St., Davenport, IA , 52803, USA

    Ilwoo Cho

  2. Department of Mathematics, 418 Ambrose Hall, Saint Ambrose University, 518 W. Locust St., Davenport, IA, 52803, USA

    Timothy L. Gillespie

Authors
  1. Ilwoo Cho
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  2. Timothy L. Gillespie
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Correspondence to Ilwoo Cho.

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Communicated by Palle Jorgensen.

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Cho, I., Gillespie, T.L. Free Probability on Hecke Algebras. Complex Anal. Oper. Theory 9, 1491–1531 (2015). https://doi.org/10.1007/s11785-014-0403-1

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  • DOI: https://doi.org/10.1007/s11785-014-0403-1

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