We prove that the existence of a homogeneous invariant of degree n for a
representation of a semi-simple Lie group guarantees the existence of
non-trivial solutions of D_{\alpha} = 0: these correspond to the maximum value
of the square of the invariant divided by the norm of the representation to the
n^{th} power.Comment: 4 pages, late

Buccella, F.

English

arXiv

We prove that the existence of a homogeneous invariant of degree n for arepresentation of a semi-simple Lie group guarantees the existence ofnon-trivial solutions of D_{\alpha} = 0: these correspond to the maximum valueof the square of the invariant divided by the norm of the representation to then^{th} power

Solutions of D_\alpha - 0 from Homogeneous Invariant Functions

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