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

Martin Chaktoura; Fernando Szechtman

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

Representation Theory 2013-06-19 v1

Authors: Martin Chaktoura , Fernando Szechtman

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 $gl(V)$ 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 all its composition factors.

Keywords

composition series general linear algebra classical subalgebras bilinear forms skew-adjoint endomorphisms module theory arbitrary fields

Cite

@article{arxiv.1306.4288,
  title  = {Composition series of $\gl(m)$ as a module for its classical subalgebras over an arbitrary field},
  author = {Martin Chaktoura and Fernando Szechtman},
  journal= {arXiv preprint arXiv:1306.4288},
  year   = {2013}
}

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

Abstract

Keywords

Cite

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