Abstract Let Z (W) be the center of the finite W -algebra W (g, e) associated with g=Lie (G) and a nilpotent element e for a connected reductive algebraic group G over an algebraically closed field x1D55C of prime characteristic p under the standard hypotheses (H1) - (H3) (see 8, section 6·3). In this paper, we first demonstrate that our previous results in 20 on the structure and geometric properties of Z (W) for p0 are still true under the present weakened restriction on p. Then we study the Zassenhaus variety Z of W (g, e), which is by definition the maximal spectrum Specm (Z (W) ) of Z (W). On basis of the structure properties of Z (W), we describe Z via a good transverse slice S and show that Z is birationally equivalent to S, thereby a rational affine scheme. In the special case when e=0, we reobtain one of the main results of 26 on the rationality of the Zassenhaus varieites for reductive Lie algebras in prime characteristic.
SHU et al. (Mon,) studied this question.