Weight Varieties
Allen Knutson
I define ``weight varieties'',
the geometric analogues of weight spaces
of irreducible representations of a Lie group G.
The zero weight variety carries a natural action of the Weyl group;
I give a description of the fixed-point set of each element.
I reinterpret
the Gel'fand-MacPherson correspondence to show that certain GL_n(C)
weight varieties can be identified with moduli spaces of polygons in
R^3, and that on them the residual Gel'fand-Cetlin system has a
concrete geometrical interpretation.
Lastly, I compare those
with the moduli space of flat SU(2)
connections on an n-holed Riemann sphere.