1992/09/29 by A. N. Kirillov, Kirillov, A. N., P. Mathieu +5
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9209114
5 pages, harvmac, LETH-PHY-9/92 (LAVAL-PHY-23/92)
arxiv created 1992/09/29 · arxiv updated 2009/11/30
Motivated by a formula (due to Zelobenko) for finite Lie algebra tensor products, we propose a reformulation of the Gepner-Witten depth rule. Implementation of this rule remains difficult, however, since the basis states convenient for calculating tensor product coefficients do not have a well-defined 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.)