Counting paths in Bratteli diagrams for SU(2)_k

Details Counting paths in Bratteli diagrams for SU(2)_k Counting paths in Bratteli diagrams for SU(2)_k

2008-06-30

arxiv.org/abs/0806.4809v2

Mathematics

Combinatorics

5 pages, 3 LaTeX figures

Scientific paper

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.

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