Representations and Corresponding Operators Induced by Hecke Algebras

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• 作者：Ilwoo Cho
• 关键词：Free probability ; Free moments ; Free cumulants ; The Hecke algebra ; Normal Hecke subalgebra ; Free probability spaces ; Representations ; Operators ; Hilbert spaces
• 刊名：Complex Analysis and Operator Theory
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：10
• 期：3
• 页码：437-477
• 全文大小：730 KB
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• 作者单位：Ilwoo Cho (1)
  
  1. Department of Mathematics, 421 Ambrose Hall, Saint Ambrose University, 518 W. Locust St., Davenport, IA, 52803, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Operator Theory
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1661-8262

文摘

In this paper, by establishing free-probabilistic models on the Hecke algebras \(\mathcal {H}(G_{p})\), we construct canonical free probability spaces \((\mathcal {H}(G_{p}), \psi _{p})\), where \(G_{p} = GL_{2}(\mathbb {Q} _{p})\), for primes \(p\). Dependent upon such free-probabilistic structures, we study corresponding representations of \(\mathcal {H}(G_{p})\), and consider spectral properties of operators realized under representations.