Crystallising the Depth Rule for WZNW Fusion Coefficients
Abstract
Motivated by a formula (due to Zelobenko) for finite Lie algebra tensor products, we propose a reformulation of the GepnerWitten depth rule. Implementation of this rule remains difficult, however, since the basis states convenient for calculating tensor product coefficients do not have a welldefined depth. To avoid this problem, we present a `crystal depth rule', that gives a lower bound for the minimum level at which a WZNW fusion appears. The bound seems to be quite accurate for $su(N>3),$ and for $su(3)$ the rule is proven to be exact. (Talk presented by M.W. at the XIXth International Colloquium on Group Theoretical Methods in Physics.)
 Publication:

arXiv eprints
 Pub Date:
 September 1992
 arXiv:
 arXiv:hepth/9209114
 Bibcode:
 1992hep.th....9114K
 Keywords:

 High Energy Physics  Theory
 EPrint:
 5 pages, harvmac, LETHPHY9/92 (LAVALPHY23/92)