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

Takehiro Hasegawa, Hayato Saigo, Seiken Saito, Shingo Sugiyama
2018 Infinite Dimensional Analysis Quantum Probability and Related Topics  

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2018 pre-print arXiv:1803.02217v1 fatcat:tutnsafnvbc4picqt6gansdlyi
The subject of the present paper is an application of quantum probability to p-adic objects. We give a quantum-probabilistic interpretation of the spherical Hecke algebra for PGL_2(F), where F is a p-adic field. As a byproduct, we obtain a new proof of the Fourier inversion formula for PGL_2(F).
doi:10.1142/s0219025718500157 fatcat:wiqlhqhuirebjnrtght54p4bxe
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Takehiro Hasegawa, Hayato Saigo, Seiken Saito, Shingo Sugiyama. "A quantum probabilistic approach to Hecke algebras for 𝔭-adic PGL2." Infinite Dimensional Analysis Quantum Probability and Related Topics 21.03 (2018) 1850015