A quantum probabilistic approach to Hecke algebras for 𝔭-adic PGL2-Reference-Cited by-同舟云学术

A quantum probabilistic approach to Hecke algebras for 𝔭-adic PGL2

Published:2018-09 Issue:03 Volume:21 Page:1850015
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

Hasegawa Takehiro¹,Saigo Hayato²,Saito Seiken³,Sugiyama Shingo⁴

Affiliation:

1. Shiga University, Otsu, Shiga 520-0862, Japan

2. Nagahama Institute of Bio-Science and Technology, 1266, Tamura, Nagahama 526-0829, Japan

3. Nagoya Bunri University, 365, Maeda, Inazawa-cho, Inazawa, Aichi 492-8520, Japan

4. Department of Mathematics, College of Science and Technology, Nihon University, Suruga-Dai, Kanda, Chiyoda, Tokyo 101-8308, Japan

Abstract

The subject of the present paper is an application of quantum probability to [Formula: see text]-adic objects. We give a quantum-probabilistic interpretation of the spherical Hecke algebra for [Formula: see text], where [Formula: see text] is a [Formula: see text]-adic field. As a byproduct, we obtain a new proof of the Fourier inversion formula for [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025718500157

Reference24 articles.

1. Interacting Fock Spaces and Gaussianization of Probability Measures

2. A Family of Calabi–Yau Varieties and Potential Automorphy II

3. Automorphic Forms and Representations

4. Averages of central L-values of Hilbert modular forms with an application to subconvexity

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