The Chevalley Involution and a Duality of Weight Varieties

Details The Chevalley Involution and a Duality of Weight Varieties The Chevalley Involution and a Duality of Weight Varieties

2004-09-15

arxiv.org/abs/math/0409260v2

Mathematics

Symplectic Geometry

Scientific paper

We study the action of the Chevalley involution of a simple complex Lie group G on the set of its weight varieties (i.e. torus quotients of its flag manifolds). We find for torus quotients of Grassmannians (for GL(n)) that we obtain the classical notion of "association of projective point sets" (see Ch. III of Dolgachev-Ortland, Asterisque 165). We say a weight variety is "self-dual" if it is carried into itself by the action of the Chevalley involution. Our main theorem is a classification of those self-dual weight varieties for which the induced self-map is the identity. This problem is the "classical problem" associated to the "quantum problem" of classifying the self-dual representations V of G for which the induced action of the Chevalley involution on the zero weight space V[0] is a scalar. This latter problem is important in the study of the representation of the Artin group associated to G on V[0] obtained as the monodromy representation of the Casimir connection - see Millson - Toledano Laredo arXiv:math.QA/0305062.

Affiliated with

Also associated with

No associations

Rating

The Chevalley Involution and a Duality of Weight Varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Chevalley Involution and a Duality of Weight Varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Chevalley Involution and a Duality of Weight Varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-621876