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

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

References in corpus (1)

• Existence of Hilbert cusp forms with non-vanishing $L$-values

Cited by in corpus (1)

• The limit theorem with respect to the matrices on non-backtracking paths of a graph