McKay correspondence and the branching law for finite subgroups of $\mathbf{SL}_3\mathbb{C}$

Details McKay correspondence and the branching law for finite subgroups of $\mathbf{SL}_3\mathbb{C}$ McKay correspondence and the branching law for finite subgroups of $\mathbf{SL}_3\mathbb{C}$

2009-09-03

arxiv.org/abs/0909.0578v1

Mathematics

Representation Theory

32 pages

Scientific paper

Given $\Gamma$ a finite subgroup of $\mathbf{SL}_3\mathbb{C}$, we determine how an arbitrary finite dimensional irreducible representation of $\mathbf{SL}_3\mathbb{C}$ decomposes under the action of $\Gamma$. To the subgroup $\Gamma$ we attach a generalized Cartan matrix $C_\Gamma$. Then, inspired by B. Kostant, we decompose the Coxeter element of the Kac-Moody algebra attached to $C_\Gamma$ as a product of reflections of a special form, thereby suggesting an algebraic form for the McKay correspondence in dimension 3.

Affiliated with

Also associated with

No associations

Rating

McKay correspondence and the branching law for finite subgroups of $\mathbf{SL}_3\mathbb{C}$ 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 McKay correspondence and the branching law for finite subgroups of $\mathbf{SL}_3\mathbb{C}$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and McKay correspondence and the branching law for finite subgroups of $\mathbf{SL}_3\mathbb{C}$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-663544