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Mathematics
Vertex Algebras
1. Foundations and Motivation
2. Mathematical Preliminaries
3. Basic Structure of Vertex Algebras
4. Axioms and Fundamental Properties
5. Core Operations and Concepts
6. Fundamental Examples
7. Affine Vertex Algebras
8. Virasoro and Conformal Structure
9. Module Theory and Representations
10. Advanced Constructions
11. Intertwining Operators and Fusion
12. Zhu's Theory
13. Vertex Operator Superalgebras
14. Rationality and Finiteness
15. Moonshine and Connections
16. Computational Aspects
17. Applications and Related Areas
11.
Intertwining Operators and Fusion
11.1.
Intertwining Operator Spaces
11.1.1.
Definition and Properties
11.1.2.
Dimension Formulas
11.1.3.
Convergence Properties
11.1.4.
Analytic Continuation
11.2.
Fusion Rules
11.2.1.
Fusion Ring Structure
11.2.2.
Verlinde Formula
11.2.3.
Modular Invariance
11.2.4.
Rationality Conditions
11.3.
Braiding and Associativity
11.3.1.
Braiding Isomorphisms
11.3.2.
Associativity Constraints
11.3.3.
Pentagon and Hexagon Identities
11.3.4.
Quantum Dimensions
11.4.
Modular Properties
11.4.1.
Modular Transformations
11.4.2.
S-Matrix and T-Matrix
11.4.3.
Modular Invariant Partition Functions
11.4.4.
Galois Symmetry
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10. Advanced Constructions
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12. Zhu's Theory