
Journal of Lie Theory 27 (2017), No. 4, 969981 Copyright Heldermann Verlag 2017 Restrictions from gl_{n} to sl_{n} Jens Carsten Jantzen Matematisk Institut, Aarhus Universitet, 8000 Aarhus C, Denmark jantzen@math.au.dk Let K be an algebraically closed field, let n be a positive integer. Consider the general linear Lie algebra of all (n × n)matrices over K and its subalgebra of all matrices with trace equal to 0, the special linear Lie algebra. If the characteristic of K does not divide n, then the larger Lie algebra is the direct product of the smaller Lie algebra with a one dimensional Lie algebra; in this case each finite dimensional simple module for the general linear Lie algebra restricts to a simple module for the special linear Lie algebra. This is no longer the case when the characteristic of K divides n; the purpose of this paper is to describe what happens in this situation. Keywords: Lie algebras, representations. MSC: 17B10, 17B50 [ Fulltextpdf (283 KB)] for subscribers only. 