HIGHEST WEIGHT VECTORS WITH SMALL WEIGHTS IN THE VERTEX OPERATOR ALGEBRA ASSOCIATED WITH A LATTICE OF TYPEAl

2001 ◽  
Vol 29 (3) ◽  
pp. 1311-1324 ◽  
Author(s):  
Hiromichi Yamada
Keyword(s):  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Highest Weight

On characters of L𝔰𝔩n(−Λ0)-modules

2019 ◽  
Vol 22 (05) ◽  
pp. 1950030 ◽  
Author(s):  
Kathrin Bringmann ◽  
Karl Mahlburg ◽  
Antun Milas
Keyword(s):  
Asymptotic Expansion ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Theta Functions ◽  
Asymptotic Behaviors ◽  
Highest Weight ◽  
False Theta Functions ◽  
Decomposition Formula ◽  
Quantum Dimensions

We use recent results of Rolen, Zwegers, and the first author to study the characters of irreducible (highest weight) modules for the vertex operator algebra [Formula: see text]. We establish asymptotic behaviors of characters for the (ordinary) irreducible [Formula: see text]-modules. As a consequence, we prove that their quantum dimensions are one, as predicted by the representation theory. We also establish a full asymptotic expansion of irreducible characters for [Formula: see text]. Finally, we determine a decomposition formula for the full characters in terms of unary theta and false theta functions which allows us to study their modular properties.

scholarly journals Combinatorial bases of modules for affine Lie algebra B 2(1)

2013 ◽  
Vol 11 (2) ◽  
Author(s):  
Mirko Primc
Keyword(s):  
Lie Algebra ◽  
Vertex Operator ◽  
Vertex Operator Algebra ◽  
Intertwining Operators ◽  
Type B ◽  
Highest Weight Module ◽  
Highest Weight ◽  
Affine Lie Algebra ◽  
Algebra Theory ◽  
Simple Currents

AbstractWe construct bases of standard (i.e. integrable highest weight) modules L(Λ) for affine Lie algebra of type B 2(1) consisting of semi-infinite monomials. The main technical ingredient is a construction of monomial bases for Feigin-Stoyanovsky type subspaces W(Λ) of L(Λ) by using simple currents and intertwining operators in vertex operator algebra theory. By coincidence W(kΛ0) for B 2(1) and the integrable highest weight module L(kΛ0) for A 1(1) have the same parametrization of combinatorial bases and the same presentation P/I.

scholarly journals Uniqueness results for the moonshine vertex operator algebra

2007 ◽  
Vol 129 (2) ◽  
pp. 583-609 ◽  
Author(s):  
Chongying Dong ◽  
Robert L. Griess ◽  
Ching Hung. Lam
Keyword(s):  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Uniqueness Results ◽  
Moonshine Vertex Operator Algebra

scholarly journals VIRASORO CORRELATION FUNCTIONS FOR VERTEX OPERATOR ALGEBRAS

2012 ◽  
Vol 23 (10) ◽  
pp. 1250106 ◽  
Author(s):  
DONNY HURLEY ◽  
MICHAEL P. TUITE
Keyword(s):  
Graph Theory ◽  
Vertex Operator ◽  
Generating Functions ◽  
Operator Algebra ◽  
Correlation Functions ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Genus Zero ◽  
Genus One

We consider all genus zero and genus one correlation functions for the Virasoro vacuum descendants of a vertex operator algebra. These are described in terms of explicit generating functions that can be combinatorially expressed in terms of graph theory related to derangements in the genus zero case and to partial permutations in the genus one case.

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