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SUMMARY:Invariant forms on minuscule representations - Richard Green (Univ
 ersity of Colorado Boulder)
DTSTART:20150513T150000Z
DTEND:20150513T160000Z
UID:TALK58282@talks.cam.ac.uk
CONTACT:David Stewart
DESCRIPTION:A minuscule representation of a simple Lie algebra over the co
 mplex numbers is an irreducible representation for which the Weyl group ac
 ts transitively on the weights. Minuscule representations are often equipp
 ed 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 t
 ype $E_6$\, and a symmetric invariant quartic form on the 56-dimensional r
 epresentation in type $E_7$. I will discuss how the combinatorial structur
 e of the weights of a minuscule representation can be used to gain insight
  into these forms.
LOCATION:MR12
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