A \(\phi_{1,3}\)-filtration of the Virasoro minimal series \(M(p,p')\) with \(1<p'/p<2\).

*(English)*Zbl 1162.17025In the paper under review the authors present certain results and conjectures about basis of the minimal models \(M_{r,s} ^{(p,p')}\) for the Virasoro algebra in the case \(1 < p' /p < 2\). They study filtration of minimal models by the \((1,3)\)-primary field \(\phi_{1,3}(z)\). In order to support their conjecture, the authors prove that the character of the proposed basis coincides with the character of \(M_{r,s} ^{(p,p')}\). They also show that in the unitary case, the bi-graded character of the proposed basis and that of \(\text{gr} ^{E} M_{r,s} ^{(p,p')}\) coincide, where \(\text{gr} ^{E} M_{r,s} ^{(p,p')}\) is the associated graded space with respect to the filtration defined by \(\phi_{1,3}(z)\).

Reviewer: Dražen Adamović (Zagreb)

##### MSC:

17B68 | Virasoro and related algebras |

81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |

17B67 | Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |

##### References:

[1] | G. E. Andrews, R. J. Baxter and P. J. Forrester, Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities, J. Statist. Phys. 35 (1984), no. 3- 4, 193-266. · Zbl 0589.60093 · doi:10.1007/BF01014383 |

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