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The 3-state Potts model and Rogers-Ramanujan series

Alex Feingold, Antun Milas (2013)

Open Mathematics

We explain the appearance of Rogers-Ramanujan series inside the tensor product of two basic A 2(2) -modules, previously discovered by the first author in [Feingold A.J., Some applications of vertex operators to Kac-Moody algebras, In: Vertex Operators in Mathematics and Physics, Berkeley, November 10–17, 1983, Math. Sci. Res. Inst. Publ., 3, Springer, New York, 1985, 185–206]. The key new ingredients are (5,6)Virasoro minimal models and twisted modules for the Zamolodchikov W 3-algebra.

The $N = 1$ triplet vertex operator superalgebras: twisted sector.

Adamović, Dražen, Milas, Antun (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

The spectrum of coupled random matrices.

Adler, M., van Moerbeke, P. (1999)

Annals of Mathematics. Second Series

The Virasoro algebra and some exceptional Lie and finite groups.

Tuite, Michael P. (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Tree algebras: An algebraic axiomatization of intertwining vertex operators

Igor Kříž, Yang Xiu (2012)

Archivum Mathematicum

We describe a completely algebraic axiom system for intertwining operators of vertex algebra modules, using algebraic flat connections, thus formulating the concept of a tree algebra. Using the Riemann-Hilbert correspondence, we further prove that a vertex tensor category in the sense of Huang and Lepowsky gives rise to a tree algebra over $ℂ$ . We also show that the chiral WZW model of a simply connected simple compact Lie group gives rise to a tree algebra over $ℚ$ .