Vertex Algebras
Central Extension of Diff(S¹)
Commutation Relations
Central Charge Parameter
Highest Weight Theory
Verma Module Construction
Vertex Operator Realization
Singular Vectors
Kac Determinant
Conformal Vector Definition
Energy-Momentum Tensor
Conformal Weight Grading
Translation Properties
Primary Field Definition
Transformation Properties
Quasi-Primary Characterization
Descendant Field Construction
Weight Space Decomposition
Finite Dimensional Weight Spaces
Conformal Weight Bounds
Rationality Conditions
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7. Affine Vertex Algebras
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9. Module Theory and Representations