Crystallising the Depth Rule for WZNW Fusion Coefficients

Details Crystallising the Depth Rule for WZNW Fusion Coefficients Crystallising the Depth Rule for WZNW Fusion Coefficients

1992-09-29

arxiv.org/abs/hep-th/9209114v1

Physics

High Energy Physics

High Energy Physics - Theory

5 pages, harvmac, LETH-PHY-9/92 (LAVAL-PHY-23/92)

Scientific paper

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.)

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