arXiv subjects

M. A. Walton

Publications and source records attributed to M. A. Walton.

23 records · Page 2Linked to original sources

arXiv1995

Galois Relations on Knot Invariants

We discuss the existence of Galois relations obeyed by certain link invariants. Some of these relations have recently been identified and exploited within the context of CFT and Lie/Kac-Moody representation theory. These relations should aid in computing knot invariants. They probably have an interpretation in terms of quasitriangular (quasi-)Hopf algebras. They could also have a topological interpretation, and may serve as a concrete model for related ideas of Degiovanni, Drinfeld, Grothendieck, Ihara, and others.

q-alg↗

arXiv1994

Lie group weight multiplicities from conformal field theory

Dominant weight multiplicities of simple Lie groups are expressed in terms of the modular matrices of Wess-Zumino-Witten conformal field theories, and related objects. Symmetries of the modular matrices give rise to new relations among multiplicities. At least for some Lie groups, these new relations are strong enough to completely fix all multiplicities.

hep-th↗

arXiv1993

Berenstein-Zelevinsky triangles, elementary couplings and fusion rules

We present a general scheme for describing su(N)_k fusion rules in terms of elementary couplings, using Berenstein-Zelevinsky triangles. A fusion coupling is characterized by its corresponding tensor product coupling (i.e. its Berenstein-Zelevinsky triangle) and the threshold level at which it first appears. We show that a closed expression for this threshold level is encoded in the Berenstein-Zelevinsky triangle and an explicit method to calculate it is presented. In this way a complete solution of su(4)_k fusion rules is obtained.

hep-th↗

arXiv1992

Crystallising the Depth Rule for WZNW Fusion Coefficients

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.)

hep-th↗

arXiv1992

su(3)k fusion coefficients

A closed and explicit formula for all $\su{(3)}_k$ fusion coefficients is presented which, in the limit $k \rightarrow \infty$, turns into a simple and compact expression for the $su(3)$ tensor product coefficients. The derivation is based on a new diagrammatic method which gives directly both tensor product and fusion coefficients.

hep-th↗