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Are there any applications of classical groups in subjects like algebraic geometry, algebraic number theory, algebraic topology or arithmetic geometry? If there is, then can anyone please give some references? Actually, I want to do a project on that topic, so I was wondering whether there are applications that I can look forward to. And what I can read after reading classical groups that will be useful if in future I work on any of the subjects that I mentioned above?

Thank you

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Classical groups find application in the local Langlands correspondence: "Using the results of Colette Moeglin on the representations of p-adic classical groups (based on methods of James Arthur) and its relation with representations of affine Hecke algebras established by the author, we show that the category of smooth complex representations of a quasi-split p-adic classical group and its pure inner forms is naturally decomposed into subcategories which are equivalent to a tensor product of categories of unipotent representations of classical groups. A statement of this kind had been conjectured by G. Lusztig. All classical groups (general linear, orthogonal, symplectic and unitary groups) appear in this context."

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