Geodesic
Composition Series of gl(m) as a Module for its Classical Subalgebras over an Arbitrary Field
Journal of Lie theory, Tome 24 (2014) no. 1, pp. 225-258

Voir la notice de l'article provenant de la source Heldermann Verlag

\def\gl{{\frak gl}} Let $F$ be an arbitrary field and let $f\colon V\times V\to F$ be a non-degenerate symmetric or alternating bilinear form defined on a finite dimensional vector space over $F$. Let $L(f)$ be the subalgebra of $\gl(V)$ formed by all skew-adjoint endomorphisms with respect to $f$. We find a composition series for the $L(f)$-module $\gl(V)$ and furnish multiple identifications for its composition factors.
Classification : 17B10, 17B05
Mots-clés : Lie algebra, bilinear form, irreducible module, composition series 
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     author = {M. Chaktoura and F. Szechtman },
     title = {Composition {Series} of gl(m) as a {Module} for its {Classical} {Subalgebras} over an {Arbitrary} {Field}},
     journal = {Journal of Lie theory},
     pages = {225--258},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JLT_2014_24_1_JLT_2014_24_1_a10/}
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M. Chaktoura; F. Szechtman . Composition Series of gl(m) as a Module for its Classical Subalgebras over an Arbitrary Field. Journal of Lie theory, Tome 24 (2014) no. 1, pp. 225-258. http://geodesic.mathdoc.fr/item/JLT_2014_24_1_JLT_2014_24_1_a10/