Unitary representations of p-adic U(5)
Confluentes Mathematici, Tome 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.

Reçu le : 2017-10-30
Accepté le : 2020-06-07
Accepté après révision le : 2020-06-29
Publié le : 2020-09-25
DOI : https://doi.org/10.5802/cml.63
Classification : 22E50,  11S85,  20G05,  20C99
Mots clés: Representations, unitary group, unitary, U(5), p-adic groups
@article{CML_2020__12_1_93_0,
     author = {Claudia Schoemann},
     title = {Unitary representations of p-adic $ U(5) $},
     journal = {Confluentes Mathematici},
     pages = {93--146},
     publisher = {Institut Camille Jordan},
     volume = {12},
     number = {1},
     year = {2020},
     doi = {10.5802/cml.63},
     language = {en},
     url = {cml.centre-mersenne.org/item/CML_2020__12_1_93_0/}
}
Claudia Schoemann. Unitary representations of p-adic $ U(5) $. Confluentes Mathematici, Tome 12 (2020) no. 1, pp. 93-146. doi : 10.5802/cml.63. https://cml.centre-mersenne.org/item/CML_2020__12_1_93_0/

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