Primitive ideals in the affinoid enveloping algebras of semisimple Lie algebras

Abstract

For a semisimple Lie algebra defined over a discrete valuation ring with field of fractions $K$, we prove that any primitive ideal with rational central character in the affinoid enveloping algebra, $\widehat{U(\mathfrak{g}{)}_K},$ is the annihilator of an affinoid highest weight module.