Geodesic
Restrictions from gln to sln
Journal of Lie theory, Tome 27 (2017) no. 4, pp. 969-981
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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.
Classification : 17B10, 17B50
Mots-clés : Lie algebras, representations 
@article{JLT_2017_27_4_JLT_2017_27_4_a3,
     author = {J. C. Jantzen},
     title = {Restrictions from gl\protect\textsubscript{n} to sl\protect\textsubscript{n}},
     journal = {Journal of Lie theory},
     pages = {969--981},
     year = {2017},
     volume = {27},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2017_27_4_JLT_2017_27_4_a3/}
}
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J. C. Jantzen. Restrictions from gln to sln. Journal of Lie theory, Tome 27 (2017) no. 4, pp. 969-981. http://geodesic.mathdoc.fr/item/JLT_2017_27_4_JLT_2017_27_4_a3/