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A $$\phi_{1,3}$$-filtration of the Virasoro minimal series $$M(p,p')$$ with $$1<p'/p<2$$. (English) Zbl 1162.17025
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 $$\phi_{1,3}(z)$$.

##### 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
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##### 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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