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arXiv · 1803.02217

A quantum probabilistic approach to Hecke algebras for $\mathfrak{p}$-adic ${\rm PGL}_2$

Takehiro Hasegawa·Hayato Saigo·Seiken Saito·Shingo Sugiyama
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Abstract

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 ${\rm PGL}_2(F)$, where $F$ is a $p$-adic field. As a byproduct, we obtain a new proof of the Fourier inversion formula for ${\rm PGL}_2(F)$.

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BibTeXRIS

Takehiro Hasegawa, Hayato Saigo, Seiken Saito, Shingo Sugiyama. 2018-03-05. A quantum probabilistic approach to Hecke algebras for $\mathfrak{p}$-adic ${\rm PGL}_2$. https://doi.org/10.1142/s0219025718500157

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