DIFFERENTIAL-OPERATORS ON VARIETIES WITH A QUOTIENT SUBVARIETY

A finite group G acts on a smooth affine variety Spec A, leaving stabl e a closed subvariety Spec A/J. The ring of functions on the variety o btained from Spec A by replacing Spec A/J by its quotient (Spec A/J)/G and leaving the complement Spec A/Spec A/J unchanged is A(G) + J. For reasonables G-actions the ring of differential operators D(A(G) + J) has a unique minimal non-zero ideal, J D(A), with the factor isomorphi c to D(A/J)G. Particular cases of this construction are considered wit h emphasis on the problem of when differential operators extend from ( A/J)G to A/J. (C) 1994 Academic Press, Inc.