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Let us consider the case when the centre acts trivially, for simplicity. Let us call $H_p$ to be the polynomial algebra generated by the classical Hecke operators $\{T_{p^r}\mid r\ge 0\}$. Using the H …

Let $D$ be a definite quaternion division algebra over $\mathbb{Q}$ and $\mathcal{O}$ be an Eichler order of $D$. Let $F$ be a Maass form in $L^2(PGL_2(\mathcal{O})\backslash PGL_2(D\otimes\mathbb{R}) …

Let $F$ be a non-Archimedean local field with ring of integers $O$, $\pi$ be a uniformizer. Let $\tilde{G}$ be a connected algebraic group over $F$ and splits over $F$, fix a split maximal torus $\til …

I am confused about the definition of Hecke operators. It will be great if someone provides some references. Shimura's 'Arithmetic Theory of Automorphic forms' says: Let $\Gamma$ be acting in the lef …