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Journal of Lie Theory 27 (2017), No. 4, 969--981 Copyright Heldermann Verlag 2017 Restrictions from gln to sln 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 [ Fulltext-pdf (283 KB)] for subscribers only. |