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

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  • Takehiro Hasegawa
    Shiga University, Otsu, Shiga 520-0862, Japan
  • Hayato Saigo
    Nagahama Institute of Bio-Science and Technology, 1266, Tamura, Nagahama 526-0829, Japan
  • Seiken Saito
    Nagoya Bunri University, 365, Maeda, Inazawa-cho, Inazawa, Aichi 492-8520, Japan
  • Shingo Sugiyama
    Department of Mathematics, College of Science and Technology, Nihon University, Suruga-Dai, Kanda, Chiyoda, Tokyo 101-8308, Japan

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<jats:p>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].</jats:p>

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