Harish-Chandra invariants and the centre of the reduced enveloping algebra

Abstract

In this article we consider the centre of the reduced enveloping algebra of the Lie algebra of a reductive algebraic group in very good characteristic p > 2. The Harish-Chandra centre maps to the centre of each reduced enveloping algebra and, using a combination of induction and deformation arguments, we describe precisely for which p-characters this map is surjective: it is if and only if the chosen character is regular. This provides the converse to a theorem of Mirković and Rumynin.

arXiv commentThe assumptions have been weakened in this version by improving proof of the main theorem; 11 pages; accepted for publication in the Journal of Pure and Applied Algebra