The invariant polynomials on simple Lie superalgebras

Details The invariant polynomials on simple Lie superalgebras The invariant polynomials on simple Lie superalgebras

1998-10-17

arxiv.org/abs/math/9810111v1

Mathematics

Representation Theory

28 p., Latex

Scientific paper

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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