geometric representation theory
representation, 2-representation, ∞-representation
Grothendieck group, lambda-ring, symmetric function, formal group
principal bundle, torsor, vector bundle, Atiyah Lie algebroid
Eilenberg-Moore category, algebra over an operad, actegory, crossed module
Be?linson-Bernstein localization?
Let be a Lie group which is compact and connected. Write for the maximal torus subgroup.
A weight on is an irreducible representation of the maximal torus subgroup .
For a representation of , and for a weight, the weight space of with respect to is the subspace of which as a representation of is a direct sum of -s.
In other words, the weight space of a -representation for a weight is the corresponding eigenspace under the action of .
For connected compact Lie groups the
Peter Woit, Topics in representation theory: Roots and weights (pdf)
Wikipedia, Weight (representation theory)
Last revised on March 29, 2014 at 09:02:28. See the history of this page for a list of all contributions to it.