On sums of tensor and fusion multiplicities

Details On sums of tensor and fusion multiplicities On sums of tensor and fusion multiplicities

2011-03-15

arxiv.org/abs/1103.2943v2

J.Phys.A44:295208,2011

Physics

Mathematical Physics

28 pages, 1 figure, LaTeX; corrected typos, added references, shortened appendix A and section 3.3, added comments in section

Scientific paper

10.1088/1751-8113/44/29/295208

The total multiplicity in the decomposition into irreducibles of the tensor product i x j of two irreducible representations of a simple Lie algebra is invariant under conjugation of one of them sum_k N_{i j}^{k}= sum_k N_{ibar j}^{k}. This also applies to the fusion multiplicities of affine algebras in conformal WZW theories. In that context, the statement is equivalent to a property of the modular S matrix, Sigma(k)= sum_j S_{j k}=0 if k is a complex representation. Curiously, this vanishing of Sigma(k) also holds when k is a quaternionic representation. We provide proofs of all these statements. These proofs rely on a case-by-case analysis, maybe overlooking some hidden symmetry principle. We also give various illustrations of these properties in the contexts of boundary conformal field theories, integrable quantum field theories and topological field theories.

Affiliated with

Also associated with

No associations

Rating

On sums of tensor and fusion multiplicities 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 On sums of tensor and fusion multiplicities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On sums of tensor and fusion multiplicities will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-139158