Composition Series of gl(m) as a Module for its Classical Subalgebras over an Arbitrary Field

M. Chaktoura; F. Szechtman

doi:10.5802/jolt.783

M. Chaktoura; F. Szechtman

Journal of Lie Theory, Volume 24 (2014) no. 1, pp. 225-258

Abstract

\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.

arXiv Zbl

DOI: 10.5802/jolt.783

Classification: 17B10, 17B05
Keywords: Lie algebra, bilinear form, irreducible module, composition series

@article{JOLT_2014_24_1_a10,
     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},
     year = {2014},
     volume = {24},
     number = {1},
     doi = {10.5802/jolt.783},
     zbl = {1327.17005},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.783/}
}

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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, Volume 24 (2014) no. 1, pp. 225-258. doi: 10.5802/jolt.783

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