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Irreducible dual of p-adic U(5)

Representation Theory 2014-11-21 v1

Abstract

We study the parabolically induced complex representations of the unitary group in 5 variables, U(5), U(5), defined over a p-adic field. Let F F be a p-adic field. Let E:F E : F be a field extension of degree two. Let Gal(E:F)={1,σ}. Gal(E : F ) = \{ 1 , \sigma \}. We write σ(x)=x  xE. \sigma(x) = \overline{x} \; \forall x \in E. Let E:=E{0} E^* := E \setminus \{ 0 \} and let E1:={xExx=1}. E^1 := \{x \in E \mid x \overline{x} = 1 \}. U(5) U(5) has three proper standard Levi subgroups, the minimal Levi subgroup M0E×E×E1 M_0 \cong E^* \times E^* \times E^1 and the two maximal Levi subgroups M1GL(2,E)×E1 M_1 \cong GL(2, E) \times E^1 and M2E×U(3). M_2 \cong E^* \times U(3). We consider representations induced from M0 M_0 and from non-cuspidal, not fully-induced representations of M1 M_1 and M2. M_2. We determine the points and lines of reducibility and the irreducible subquotients of these representations.

Keywords

Cite

@article{arxiv.1411.5570,
  title  = {Irreducible dual of p-adic U(5)},
  author = {Claudia Schoemann},
  journal= {arXiv preprint arXiv:1411.5570},
  year   = {2014}
}

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34 pages