Geodesic
Exotic Monoidal Structures and Abstractly Automorphic Representations for $\mathrm {GL}(2)$
Forum of Mathematics, Pi, Tome 11 (2023)

Voir la notice de l'article provenant de la source Cambridge University Press

We use the theta correspondence to study the equivalence between Godement–Jacquet and Jacquet–Langlands L-functions for ${\mathrm {GL}}(2)$. We show that the resulting comparison is in fact an expression of an exotic symmetric monoidal structure on the category of ${\mathrm {GL}}(2)$-modules. Moreover, this enables us to construct an abelian category of abstractly automorphic representations, whose irreducible objects are the usual automorphic representations. We speculate that this category is a natural setting for the study of automorphic phenomena for ${\mathrm {GL}}(2)$, and demonstrate its basic properties.This paper is a part of the author’s thesis [4]. 
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     title = {Exotic {Monoidal} {Structures} and {Abstractly} {Automorphic} {Representations} for $\mathrm {GL}(2)$},
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Gal Dor. Exotic Monoidal Structures and Abstractly Automorphic Representations for $\mathrm {GL}(2)$. Forum of Mathematics, Pi, Tome 11 (2023). doi: 10.1017/fmp.2023.18

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