A bijection between paths for the M(p,2p+1) minimal model Virasoro characters

Abstract

The states in the irreducible modules of the minimal models can be represented by infinite lattice paths arising from consideration of the corresponding RSOS statistical models. For the M(p,2p+1) models, a completely different path representation has been found recently, this one on a half-integer lattice; it has no known underlying statistical-model interpretation. The correctness of this alternative representation has not yet been demonstrated, even at the level of the generating functions, since the resulting fermionic characters differ from the known ones. This gap is filled here, with the presentation of two versions of a bijection between the two path representations of the M(p,2p+1) states. In addition, a half-lattice path representation for the M(p+1,2p+1) models is stated, and other generalisations suggested.

20 pages

References in corpus (5)

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Cited by in corpus (6)

• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Half-lattice paths and Virasoro characters
• A quartet of fermionic expressions for $M(k,2k\pm 1)$ Virasoro characters via half-lattice paths
• Path representation of su(2)_k states II: Operator construction of the fermionic character and spin-1/2--RSOS factorization
• Path representation of su(2)_k states I: Operators and particles for k=1,2
• One-Dimensional Sums and Finitized Characters of $2\times 2$ Fused RSOS Models