Composition series of $\gl(m)$ as a module for its classical subalgebras over an arbitrary field

Martin Chaktoura; Fernando Szechtman

paper

Composition series of $\gl(m)$ as a module for its classical subalgebras over an arbitrary field

arXiv:1306.4288

Abstract

Let $F$ be an arbitrary field and let $f : V \times V \to F$ be a non-degenerate symmetric or alternating bilinear form defined on an $F$ -vector space of finite dimension $m \geq 2$ . Let $L (f)$ be the subalgebra of $g l (V)$ formed by all skew-adjoint endomorphisms with respect to $f$ . We find a composition series for the $L (f)$ -module $g l (V)$ and furnish multiple identifications for all its composition factors.