  We extend two well-known results on primitive ideals in enveloping algebras
of semisimple Lie algebras, the `Irreducibility theorem' and `Duflo theorem',
to much wider classes of algebras. Our general version of Irreducibility
theorem says that if A is a positively filtered associative algebra such that
gr(A) is a commutative Poisson algebra with finitely many symplectic leaves,
then the associated variety of any primitive ideal in A is the closure of a
single connected symplectic leaf. Our general version of Duflo theorem says
that if A is an algebra with a `triangular structure' (see sect. 2), then any
primitive ideal in A is the annihilator of a simple highest weight module.
Applications to Symplectic reflection algebras and Cherednik algebras are
discussed.
