We study the parabolically induced complex representations of the unitary group in 5 variables, defined over a -adic field.
Let be a -adic field. Let be a field extension of degree two. has three proper standard Levi subgroups, the minimal Levi subgroup and the two maximal Levi subgroups and .
We consider representations induced from , representations induced from non-cuspidal, not fully-induced representations of and and representations induced from cuspidal representations of
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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Keywords: Representations, unitary group, unitary, $U(5)$, $p$-adic groups
Claudia Schoemann 1
@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 = {https://cml.centre-mersenne.org/articles/10.5802/cml.63/} }
TY - JOUR AU - Claudia Schoemann TI - Unitary representations of p-adic $ U(5) $ JO - Confluentes Mathematici PY - 2020 SP - 93 EP - 146 VL - 12 IS - 1 PB - Institut Camille Jordan UR - https://cml.centre-mersenne.org/articles/10.5802/cml.63/ DO - 10.5802/cml.63 LA - en ID - CML_2020__12_1_93_0 ER -
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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