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Half-lattice Paths and Virasoro Characters

Blondeau-Fournier O., Mathieu P., Welsh T. A.

Fundamenta Informaticae

2012

Vol. 117, nr 1-4

57-83

We first briefly review the role of lattice paths in the derivation of fermionic expressions for the M(p, p')minimalmodel characters of the Virasoro Lie algebra. We then focus on the recently introduced half-lattice paths for the M(p, 2pš1) characters, reformulating them in such a way that the two cases may be treated uniformly. That the generating functions of these half-lattice paths are indeed M(p, 2p š 1) characters is proved by describing weight preserving bijections between them and the corresponding RSOS lattice paths. Here, the M(p, 2p - 1) case is derived for the first time. We then apply the methods of Bressoud and Warnaar to these half-lattice paths to derive fermionic expressions for the Virasoro characters [...] We first briefly review the role of lattice paths in the derivation of fermionic expressions for theM(p, p')minimalmodel characters of the Virasoro Lie algebra. We then focus on the recently introduced half-lattice paths for theM(p, 2pš1) characters, reformulating them in such a way that the two cases may be treated uniformly. That the generating functions of these half-lattice paths are indeedM(p, 2p š 1) characters is proved by describing weight preserving bijections between them and the corresponding RSOS lattice paths. Here, theM(p, 2p - 1) case is derived for the first time. We then apply the methods of Bressoud and Warnaar to these half-lattice paths to derive fermionic expressions for the Virasoro characters[...] that differ from those obtained from the RSOS paths.hat differ from those obtained from the RSOS paths.