Counting paths in Bratteli diagrams for SU(2)kT. Mansour1 and S. Severini2
1 Department of Mathematics, University of Haifa - Haifa 31905, Israel
2 Institute for Quantum Computing and Department of Combinatorics & Optimization, University of Waterloo Waterloo N2L 3G1, Canada
received 30 January 2009; accepted in final form 9 April 2009; published May 2009
published online 15 May 2009
It is known that the Hilbert space dimensionality for quasiparticles in an SU(2)k Chern-Simons-Witten theory is given by a 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.
31.15.xm - Quasiparticle methods.
02.10.Ox - Combinatorics; graph theory.
© EPLA 2009