CENTRALLY GENERATED PRIMITIVE IDEALS OF U(n$$ \mathfrak{n} $$) IN TYPES B AND D

Abstract

We study the centrally generated primitive ideals of U($$ \mathfrak{n} $$), where $$ \mathfrak{n} $$ is the (locally) nilpotent radical of a (splitting) Borel subalgebra of a simple complex Lie algebra $$ \mathfrak{g} $$ = $$ \mathfrak{so} $$2n+1(ℂ), $$ \mathfrak{so} $$2n(ℂ), $$ \mathfrak{so} $$∞(ℂ). In the infinite-dimensional setting, there are infinitely many isomorphism classes of Lie algebras $$ \mathfrak{n} $$, and we fix $$ \mathfrak{n} $$ with the “largest possible” center of U($$ \mathfrak{n} $$). We characterize the centrally generated primitive ideals of U($$ \mathfrak{n} $$) in terms of the Dixmier map and the Kostant cascade.