Normality of orthogonal and symplectic nilpotent orbit closures in positive characteristic》.pdfVIP

Journal of Algebra 443 (2015) 33–48 Contents lists available at ScienceDirect Journal of Algebra /locate/jalgebra Normality of orthogonal and symplectic nilpotent orbit closures in positive characteristic ✩ Husileng Xiao ∗ , Bin Shu Department of Mathematics, East China Normal University, Shanghai 200241, China a r t i c l e i n f o a b s t r a c t Article history: In this note we investigate the normality of closures of orthog- Received 10 January 2015 onal and symplectic nilpotent orbits in positive characteristic. Available online xxxx We prove that the closure of such a nilpotent orbit is normal Communicated by Shrawan Kumar provided that neither type d nor type e minimal irreducible de- MSC: generation occurs in the closure, and conversely if the closure 17B08 is normal, then any type e minimal irreducible degeneration 17L45 does not occur in it. Here, the minimal irreducible degenera- 14L35 tions of a nilpotent orbit are introduced by W. Hesselink in [7] (or see [11] from which we take Table 1 for the complete list Keywords: of all minimal irreducible degenerations). Our result is a weak Orthogonal symplectic groups version in positive characteristic of [11, Theorem 16.2(ii)], one Nilpotent orbit closures of the main results of [11] over complex numbers. Normality