scholarly journals Quantum dimensions and fusion rules for parafermion vertex operator algebras

2015 ◽  
Vol 144 (4) ◽  
pp. 1483-1492 ◽  
Author(s):  
Chongying Dong ◽  
Qing Wang
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Fusion Rules ◽  
Quantum Dimensions

scholarly journals Fusion Rules for the Vertex Operator Algebras M(1)+ and V+L

2004 ◽  
Vol 253 (1) ◽  
pp. 171-219 ◽  
Author(s):  
Toshiyuki Abe ◽  
Chongying Dong ◽  
Haisheng Li
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Fusion Rules

scholarly journals VERTEX OPERATOR ALGEBRAS AND THE VERLINDE CONJECTURE

2008 ◽  
Vol 10 (01) ◽  
pp. 103-154 ◽  
Author(s):  
YI-ZHI HUANG
Keyword(s):  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Fusion Rules ◽  
Verlinde Formula ◽  
Modular Transformation ◽  
The Matrix ◽  
Completely Reducible

We prove the Verlinde conjecture in the following general form: Let V be a simple vertex operator algebra satisfying the following conditions: (i) V(n) = 0 for n < 0, V(0) = ℂ1 and V′ is isomorphic to V as a V-module. (ii) Every ℕ-gradable weak V-module is completely reducible. (iii) V is C2-cofinite. (In the presence of Condition (i), Conditions (ii) and (iii) are equivalent to a single condition, namely, that every weak V-module is completely reducible.) Then the matrices formed by the fusion rules among the irreducible V-modules are diagonalized by the matrix given by the action of the modular transformation τ ↦ -1/τ on the space of characters of irreducible V-modules. Using this result, we obtain the Verlinde formula for the fusion rules. We also prove that the matrix associated to the modular transformation τ ↦ -1/τ is symmetric.

Sign in / Sign up

Export Citation Format

Share Document