Feigin, B.; Feigin, E.; Jimbo, M.; Miwa, T.; Takeyama, Y. A \(\phi_{1,3}\)-filtration of the Virasoro minimal series \(M(p,p')\) with \(1<p'/p<2\). (English) Zbl 1162.17025 Publ. Res. Inst. Math. Sci. 44, No. 2, 213-257 (2008). In 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) Cited in 6 Documents 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 Keywords:Virasoro algebra; minimal models; basis; primary fields PDFBibTeX XMLCite \textit{B. Feigin} et al., Publ. Res. Inst. Math. Sci. 44, No. 2, 213--257 (2008; Zbl 1162.17025) Full Text: DOI arXiv 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.