Overrings of primitive factor rings of U(sl(2, [formula omitted]))

Abstract

This paper shows that certain primitive factor rings of U(sl(2, C )) embed in the rings of differential operators D on the curves y 2= x 2 n+1 . There is an action of SL(2, C ) as automorphisms of D making D a (sl(2)×sl(2),SL(2)) Harish-Chandra bimodule in such a way that the invariant subring under the centre of SL(2), D C 2 , is the primitive factor of U(sl(2)). This result describes all the Dixmier algebras for SL(2, C ).