Counting paths in Bratteli diagrams for SU(2)_k
arXiv:0806.4809 · doi:10.1209/0295-5075/86/33001
Abstract
It is known that the Hilbert space dimensionality for quasiparticles in an SU(2)_k Chern-Simons-Witten theory is given by the number of directed paths in certain Bratteli diagrams. We present an explicit formula for these numbers for arbitrary k. This is on the basis of a relation with Dyck paths and Chebyshev polynomials.
5 pages, 3 LaTeX figures