The invariant polynomials on simple Lie superalgebras

1998/10/17 by A. N. Sergeev, Alexander Sergeev, Sergeev, Alexander · 3 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.AC #math.RT #msc:13A50 #msc:17A70 #msc:17B35

paper · pdf · doi:10.48550/arxiv.math/9810111

28 p., Latex

arxiv created 1998/10/17 · arxiv updated 2009/11/30

Abstract

Chevalley's theorem states that for any simple finite dimensional Lie algebra G (1) the restriction homomorphism of the algebra of polynomials on G onto the Cartan subalgebra H induces an isomorphism between the algebra of G-invariant polynomials on G with the algebra of W-invariant polynomals on H, where W is the Weyl group of G, (2) each G-invariant polynomial is a linear combination of the powers of traces tr r(x), where r is a finite dimensional representation of G. None of these facts is necessarily true for simple Lie superalgebras. We reformulate Chevalley's theorem so as to embrace Lie superalgebras. Chevalley's theorem for anti-invariant polynomials is also given.

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