Irreducible dual of p-adic U(5) (1411.5570v1)

Abstract: 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. Let $ Gal(E : F ) = { 1 , \sigma }. $ We write $ \sigma(x) = \overline{x} \; \forall x \in E. $ Let $ E^* := E \setminus { 0 } $ and let $ E^1 := {x \in E \mid x \overline{x} = 1 }. $ $ U(5) $ has three proper standard Levi subgroups, the minimal Levi subgroup $ M_0 \cong E^* \times E^* \times E^1 $ and the two maximal Levi subgroups $ M_1 \cong GL(2, E) \times E^1 $ and $ M_2 \cong E^* \times U(3). $ We consider representations induced from $ M_0 $ and from non-cuspidal, not fully-induced representations of $ M_1 $ and $ M_2. $ We determine the points and lines of reducibility and the irreducible subquotients of these representations.