Primitive ideals in 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. In the case n>0, we characterise all the primitive ideals in the affinoid algebra widehat{U(mathfrak {{g}})_{n,K}}.