Infinite Kostant cascades and centrally generated primitive ideals of U(n) in types A∞, C∞

الأصل · EN

We study the center of U(n), where n is the locally nilpotent radical of a splitting Borel subalgebra of a simple complex Lie algebra g=sl∞(C), so∞(C), sp∞(C). There are infinitely many isomorphism classes of Lie algebras n, and we provide explicit generators of the center of U(n) in all cases. We then fix n with "largest possible" center of U(n) and characterize the centrally generated primitive ideals of U(n) for g=sl∞(C), sp∞(C) in terms of the above generators. As a preliminary result, we provide a characterization of the centrally generated primitive ideals in the enveloping algebra of the nilradical of a Borel subalgebra of slₙ(C), sp₂ₙ(C).