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

2013/06/18 by Martin Chaktoura, Chaktoura, Martin, Fernando Szechtman +1
Mathematics · #FOS: Mathematics #Primary 17B10 #Representation Theory (math.RT) #Secondary 17B05 #math.RT #msc:17B05 #msc:17B10

paper · pdf · doi:10.48550/arxiv.1306.4288

arxiv created 2013/06/18 · arxiv updated 2013/06/19

Abstract

Let F be an arbitrary field and let f:V× V→ F be a non-degenerate symmetric or alternating bilinear form defined on an F-vector space of finite dimension m≥ 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.

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