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Supercuspidal representations of GL(n) over a non-archimedean local field : distinction by a unitary or orthogonal subgroup, base change and automorphic induction

Abstract : In this thesis, we consider several concrete examples of the relation among the local Langlands correspondence, its functoriality and the problem of distinction. Let F/F_0 be a finite cyclic extension of non-archimedean locally compact fields of residue characteristic p and let R be an algebraically closed field of characteristic l different from p. In the first part, we assume F/F_0 to be quadratic and p to be odd, and we study the irreducible representations of GL_n(F) over R distinguished by a unitary subgroup. We completely solve the problem for supercuspidal representations and get partial results for generic representations. Meanwhile we also define an l-modular version of the cyclic base change lift. In the second part, we assume F=F_0 and p odd, and we fully characterize the complex supercuspidal representations of GL_n(F) distinguished by an orthogonal subgroup. In the final part for F/F_0 tamely ramified, we study the base change lift and the automorphic induction for complex supercuspidal representations via the simple type theory.
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Submitted on : Wednesday, November 24, 2021 - 5:46:30 PM
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  • HAL Id : tel-03447637, version 1

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Jiandi Zou. Supercuspidal representations of GL(n) over a non-archimedean local field : distinction by a unitary or orthogonal subgroup, base change and automorphic induction. Number Theory [math.NT]. Université Paris-Saclay, 2021. English. ⟨NNT : 2021UPASM030⟩. ⟨tel-03447637⟩

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