“…We say that a genuine irreducible representation π of G occurs in the theta correspondence for the dual pair (G, G ) if π occurs as a quotient of ω. The maximal quotient of ω which is π-isotypic has the form π ⊗Θ(π, W m ), where Θ(π, W m ) is a smooth representation of G [MVW,2.III.5]. The Howe duality principle asserts that Θ(π, W m ) has a unique irreducible quotient, denoted by θ(π, W m ).…”