Unitary representations of p-adic U(5)
Confluentes Mathematici, Volume 12 (2020) no. 1, pp. 93-146.

We study the parabolically induced complex representations of the unitary group in 5 variables,U(5), defined over a p-adic field.

Let F be a p-adic field. Let E:F be a field extension of degree two. U(5) has three proper standard Levi subgroups, the minimal Levi subgroup M 0 E * ×E * ×E 1 and the two maximal Levi subgroups M 1 GL(2,E)×E 1 and M 2 E * ×U(3).

We consider representations induced from M 0 , representations induced from non-cuspidal, not fully-induced representations of M 1 and M 2 and representations induced from cuspidal representations of M 1 .

We determine the points and lines of reducibility and the irreducible subquotients of these representations. Further we describe - except several particular cases - the unitary dual in terms of Langlands quotients.

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DOI: 10.5802/cml.63
Classification: 22E50, 11S85, 20G05, 20C99
Keywords: Representations, unitary group, unitary, $U(5)$, $p$-adic groups

Claudia Schoemann 1

1 Leibniz Universität Hannover, Institut für Algebraische Geometrie, Welfengarten 1, D-30167 Hannover, Germany
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Claudia Schoemann. Unitary representations of p-adic $ U(5) $. Confluentes Mathematici, Volume 12 (2020) no. 1, pp. 93-146. doi : 10.5802/cml.63. https://cml.centre-mersenne.org/articles/10.5802/cml.63/

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