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Classical Hecke operators and Hecke algebra of type $A_1$

What's the relation between the classical Hecke operators (as defined in J. P. Serre's A course in arithmetic chapter 6) and the Hecke algebra of type $A_1$, i.e. the algebra generated by the vertices ...
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Global irreducible admissible representations analogue

Let ${A}_{\mathbb{Q}}$ denote the adele over the rational numbers. Then it is known that cuspidal modular forms of level $N$ correspond to some unitary automorphic representation of $\operatorname{GL}...
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