Invariant forms on minuscule representations

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• Richard Green (University of Colorado Boulder)
• Wednesday 13 May 2015, 16:00-17:00
• MR12.

If you have a question about this talk, please contact David Stewart.

A minuscule representation of a simple Lie algebra over the complex numbers is an irreducible representation for which the Weyl group acts transitively on the weights. Minuscule representations are often equipped with invariant multilinear forms that are invariant under the action of the Lie algebra. These include symplectic or orthogonal bilinear forms, as well as an invariant cubic form on a 27-dimensional representation in type $E_6$, and a symmetric invariant quartic form on the 56-dimensional representation in type $E_7$. I will discuss how the combinatorial structure of the weights of a minuscule representation can be used to gain insight into these forms.

This talk is part of the Algebra and Representation Theory Seminar series.

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