a quartet of fermionic expressions for m(k,2k±1) virasoro characters via half-lattice paths
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2017
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Abstract
We derive new fermionic expressions for the characters of the Virasoro minimal models M(k,2k±1) by analysing the recently introduced half-lattice paths. These fermionic expressions display a quasiparticle formulation characteristic of the ϕ2,1 and ϕ1,5 integrable perturbations. We find that they arise by imposing a simple restriction on the RSOS quasiparticle states of the unitary models M(p,p+1). In fact, four fermionic expressions are obtained for each generating function of half-lattice paths of finite length L, and these lead to four distinct expressions for most characters χr,sk,2k±1. These are direct analogues of Melzer's expressions for M(p,p+1), and their proof entails revisiting, reworking and refining a proof of Melzer's identities which used combinatorial transforms on lattice paths.
We also derive a bosonic version of the generating functions of length L half-lattice paths, this expression being notable in that it involves q-trinomial coefficients. Taking the L→∞ limit shows that the generating functions for infinite length half-lattice paths are indeed the Virasoro characters χr,sk,2k±1.
| Reference Key |
blondeau-fournier2017nucleara
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|---|---|
| Authors | ;Olivier Blondeau-Fournier;Pierre Mathieu;Trevor A. Welsh |
| Journal | biology and fertility of soils |
| Year | 2017 |
| DOI |
10.1016/j.nuclphysb.2017.09.023
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