Counting paths in Bratteli diagrams for SU(2)k
Abstract
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.
- Publication:
-
EPL (Europhysics Letters)
- Pub Date:
- May 2009
- DOI:
- 10.1209/0295-5075/86/33001
- arXiv:
- arXiv:0806.4809
- Bibcode:
- 2009EL.....8633001M
- Keywords:
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- Mathematics - Combinatorics;
- Quantum Physics
- E-Print:
- 5 pages, 3 LaTeX figures