Journal of Lie Theory 24 (2014), No. 1, 225--258
Copyright Heldermann Verlag 2014
Composition Series of gl(m) as a Module for its Classical Subalgebras over an Arbitrary Field
Martin Chaktoura
Dept. of Mathematics and Statistics, University of Regina, 3737 Wascana Pkwy, Regina, SK S4S 0A2, Canada
martin_chaktoura@yahoo.com.ar
Fernando Szechtman
Dept. of Mathematics and Statistics, University of Regina, 3737 Wascana Pkwy, Regina, SK S4S 0A2, Canada
fernando.szechtman@gmail.com
[Abstract-pdf]
\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.
Keywords: Lie algebra, bilinear form, irreducible module, composition series.
MSC: 17B10; 17B05
[ Fulltext-pdf (407 KB)] for subscribers only.