On primitive ideals

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