Displaying similar documents to “Vertex algebras and algebraic curves”

A family of regular vertex operator algebras with two generators

Dražen Adamović (2007)

Open Mathematics

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For every m ∈ ℂ ∖ 0, −2 and every nonnegative integer k we define the vertex operator (super)algebra D m,k having two generators and rank 3 m m + 2 . If m is a positive integer then D m,k can be realized as a subalgebra of a lattice vertex algebra. In this case, we prove that D m,k is a regular vertex operator (super) algebra and find the number of inequivalent irreducible modules.

The 3-state Potts model and Rogers-Ramanujan series

Alex Feingold, Antun Milas (2013)

Open Mathematics

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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. ...

Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products

Pavel Etingof, Wee Liang Gan, Victor Ginzburg, Alexei Oblomkov (2007)

Publications Mathématiques de l'IHÉS

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The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection...

Tree algebras: An algebraic axiomatization of intertwining vertex operators

Igor Kříž, Yang Xiu (2012)

Archivum Mathematicum

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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 .