Journal of Lie Theory

no. 4
Restrictions from gln to sln
Journal of Lie Theory, Volume 27 (2017) no. 4, pp. 969-981
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.
DOI: 10.5802/jolt.977
Classification: 17B10, 17B50
Keywords: Lie algebras, representations 
@article{JOLT_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},
     doi = {10.5802/jolt.977},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.977/}
}
TY  - JOUR
AU  - J. C. Jantzen
TI  - Restrictions from gln to sln
JO  - Journal of Lie Theory
PY  - 2017
SP  - 969
EP  - 981
VL  - 27
IS  - 4
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.977/
DO  - 10.5802/jolt.977
ID  - JOLT_2017_27_4_a3
ER  - 
%0 Journal Article
%A J. C. Jantzen
%T Restrictions from gln to sln
%J Journal of Lie Theory
%D 2017
%P 969-981
%V 27
%N 4
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.977/
%R 10.5802/jolt.977
%F JOLT_2017_27_4_a3
J. C. Jantzen. Restrictions from gln to sln. Journal of Lie Theory, Volume 27 (2017) no. 4, pp. 969-981. doi: 10.5802/jolt.977

Cited by Sources: