Globalization of supercuspidal representations over function fields and applications

Gan, Wee Teck; Lomelí, Luis

doi:10.4171/jems/825

Cited by 23 publications

(13 citation statements)

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“…For condition (b), since we only care about the case when χ = 1, it is automatically satisfied. Thus, if we use [13], Theorem 1.3 to replace [18], Theorem 1 and follow the proof in [18], then we finish the proof when R = C and F/F 0 is a quadratic extension of locally compact fields of characteristic p.…”

Section: Distinction Implies Galois Invariance For a Supercuspidal Re...mentioning

confidence: 90%

“…If char(F ) > 0, in order to use the proof of Hakim-Murnaghan, we only need a variant of globalization theorem for characteristic positive case. Fortunately, Gan-Lomelí already built up such kind of result for general reductive groups over function fields and locally compact fields of characteristic positive (see [13], Theorem 1.3). Following their settings, we choose the reductive group H to be R K/K0 (GL n (K)), where K/K 0 is a quadratic extension of function fields, and R K/K0 is the Weil restriction.…”

Section: Distinction Implies Galois Invariance For a Supercuspidal Re...mentioning

confidence: 99%

“…When char(F ) = p > 0, we may keep the original proof except that we need a characteristic p version of the globalization theorem. Fortunately we can use a more general result due to Gan-Lomelí [13] to get the result we need. Since each supercuspidal representation of G over a characteristic 0 algebraically closed field can be realized as a representation over Q up to multiplying an unramified character, we finish the proof when char(R) = 0.…”

Section: Introductionmentioning

confidence: 99%

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Supercuspidal representations of $\mathrm{GL}_{n}(F)$ distinguished by a unitary involution

Zou¹

2019

Preprint

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Let F/F0 be a quadratic extension of non-archimedean locally compact fields of residue characteristic p = 2. Let R be an algebraically closed field of characteristic different from p. For π a supercuspidal representation of G = GLn(F ) over R and G τ a unitary group in n variables contained in G, we prove that π is distinguished by G τ if and only if π is Galois invariant. When R = C and F is a p-adic field, this result first as a conjecture proposed by Jacquet was proved in 2010's by Feigon-Lapid-Offen by using global method. Our proof is local which works for both complex case and l-modular case with l = p. We further study the dimension of HomGτ (π, 1) and show that it is at most one.

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Section: Distinction Implies Galois Invariance For a Supercuspidal Re...mentioning

confidence: 90%

Section: Distinction Implies Galois Invariance For a Supercuspidal Re...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Supercuspidal representations of $\mathrm{GL}_{n}(F)$ distinguished by a unitary involution

Zou¹

2019

Preprint

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“…We emphasize that the classification of discrete series given in [20,22] now holds unconditionally, due to results of [1], [21, Théorème 3.1.1] and [4,Theorem 7.8]. A shorter form of this classification, which covers both classical and odd general spin groups, can be found in [9].…”

Section: Introductionmentioning

confidence: 94%

Aubert duals of discrete series: the first inductive step

Matić

2019

Glas. Mat. Ser. III

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Let Gn denote either symplectic or odd special orthogonal group of rank n over a non-archimedean local field F . We provide an explicit description of the Aubert duals of irreducible representations of Gn which occur in the first inductive step in the realization of discrete series representations starting from the strongly positive ones. Our results might serve as a pattern for determination of Aubert duals of general discrete series of Gn and should produce an interesting part of the unitary dual of this group. Furthermore, we obtain an explicit form of some representations which are known to be unitarizable.

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“…From newer works of Arthur, Moeglin and Waldspurger it is now known that, in the local field of characteristic zero, cuspidal reducibility points come from 1 2 Z, and the proof, for the fields of characteristic 0, can be found in [13,Théorème 3.1.1. ], while for the fields of positive characteristic in [4,Theorem 7.8. ] in the case of classical groups.…”

Section: Introductionmentioning

confidence: 99%

Unitary dual of p-adic group SO(7) with support on minimal parabolic subgroup

Zorić

2021

Glas. Mat. Ser. III

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In this paper, the unitary dual of p-adic group SO(7) with support on minimal parabolic subgroup is determined. In explicit determination of the unitary dual the external approach is used, which represents the basic approach for finding the unitary dual, and consists of two main steps: a complete description of the non-unitary dual and the extraction of the classes of unitarizable representations among the obtained irreducible subquotients. We expect that our results will provide deeper insight into the structure of the unitary dual in the general case.

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Globalization of supercuspidal representations over function fields and applications

Cited by 23 publications

References 0 publications

Supercuspidal representations of $\mathrm{GL}_{n}(F)$ distinguished by a unitary involution

Supercuspidal representations of $\mathrm{GL}_{n}(F)$ distinguished by a unitary involution

Aubert duals of discrete series: the first inductive step

Unitary dual of p-adic group SO(7) with support on minimal parabolic subgroup

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