Primitive ideals in affinoid enveloping algebras of semisimple Lie algebras

Abstract For a semisimple Lie algebra defined over discrete valuation ring with field of fractions K , we prove that any primitive ideal rational central character in the affinoid enveloping algebra, $$\widehat{U({\mathfrak {g}})_{K}}$$ U ( g ) K ^ is annihilator an highest weight module. In case $$n>0$$ n > 0 characterise all ideals $$\widehat{U(\mathfrak {{g}})_{n,K}}$$ , .