Vertex Algebras Associated with Even Lattices

Dong, Chongying

doi:10.1006/jabr.1993.1217

Cited by 250 publications

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“…By Dong [5], there are exactly 12 isomorphism classes of irreducible V Lmodules, which are represented by V L (i,j) , i = 0, a, b, c and j = 0, 1, 2. We use the symbol e α , α ∈ L ⊥ to denote a basis of C{L ⊥ }.…”

Section: Amentioning

confidence: 99%

ℤ₃symmetry and W₃algebra in lattice vertex operator algebras

Dong

Lam²,

Tanabe³

et al. 2004

Pacific J. Math.

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Section: Amentioning

confidence: 99%

ℤ₃symmetry and W₃algebra in lattice vertex operator algebras

Dong

Lam²,

Tanabe³

et al. 2004

Pacific J. Math.

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“…We present a self-contained introduction to lattice vertex operators; we restrict ourselves to the basic results required for our proofs. There are several articles and books one can refer to in order to get a whole variety of viewpoints, for example [3,6,11,13,14,17]. In this paper, we prefer a somewhat different approach and try to follow the philosophy of the paper of Feigin and Fuchs [4], who used vertex operators to construct singular vectors in Verma modules for the Virasoro algebra.…”

Section: Outline Of the Papermentioning

confidence: 99%

Parking functions and vertex operators

Dotsenko

2008

Sel. math., New ser.

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Abstract. We introduce several associative algebras and families of vector spaces associated to these algebras. Using lattice vertex operators, we obtain dimension and character formulae for these spaces. In particular, we define a family of representations of symmetric groups which turn out to be isomorphic to parking function modules. We also construct families of vector spaces whose dimensions are Catalan numbers and Fuss-Catalan numbers respectively. Conjecturally, these spaces are related to spaces of global sections of vector bundles on (zero fibres of) Hilbert schemes and representations of rational Cherednik algebras.

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“…We also note that V L is strongly regular and the central charge of V L is equal to the rank of L. [23]. It was also proved in [7] that any irreducible V L -module is isomorphic to V α+L for some α + L ∈ L * /L. In particular, we have the following result.…”

Section: Lattice Vertex Operator Algebrasmentioning

confidence: 73%

Construction of Holomorphic Vertex Operator Algebras of Central Charge 24 Using the Leech Lattice and Level p Lattices

Lam¹,

Shimakura²

2017

Bulletin of the Inst. of Math. Academia Sinica(N.S.)

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In this article, we discuss a more uniform construction of all 71 holomorphic vertex operator algebras in Schellekens' list using an idea proposed by G. Höhn. The main idea is to try to construct holomorphic vertex operator algebras of central charge 24 using some sublattices of the Leech lattice Λ and level p lattices. We study his approach and try to elucidate his ideas. As our main result, we prove that for an even unimodular lattice L and a prime order isometry g, the orbifold vertex operator algebra Vĝ Lg has group-like fusion. We also realize the construction proposed by Höhn for some special isometry of the Leech lattice of prime order.

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Vertex Algebras Associated with Even Lattices

Cited by 250 publications

References 0 publications

ℤ₃symmetry and W₃algebra in lattice vertex operator algebras

ℤ₃symmetry and W₃algebra in lattice vertex operator algebras

Parking functions and vertex operators

Construction of Holomorphic Vertex Operator Algebras of Central Charge 24 Using the Leech Lattice and Level p Lattices

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Vertex Algebras Associated with Even Lattices

Cited by 250 publications

References 0 publications

ℤ3symmetry and W3algebra in lattice vertex operator algebras

ℤ3symmetry and W3algebra in lattice vertex operator algebras

Parking functions and vertex operators

Construction of Holomorphic Vertex Operator Algebras of Central Charge 24 Using the Leech Lattice and Level p Lattices

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ℤ₃symmetry and W₃algebra in lattice vertex operator algebras

ℤ₃symmetry and W₃algebra in lattice vertex operator algebras