Unitary Dual of p-adic U(5)

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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, σ}. We write σ(x) = x ∀ x ∈ E. Let E*:= E { 0 } and let E¹:= {x ∈ E x x = 1 }. U(5) has three proper standard Levi subgroups, the minimal Levi subgroup M₀ E* × E* × E¹ and the two maximal Levi subgroups M₁ GL(2, E) × E¹ and M₂ E* × U(3). We consider representations induced from the minimal Levi subgroup M₀, representations induced from non-cuspidal, not fully-induced representations of the two maximal Levi subgroups M₁ and M₂, and representations induced from cuspidal representations of M₁. We describe - except several particular cases - the unitary dual in terms of Langlands-quotients.