Counting paths in Bratteli diagrams for SU(2)_k

Understand

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.