2 Examples of local formal distributions 2.1 Virasoro currents and Virasoro algebra . 2.2 Affine currents and affine Lie algebras . . 2.3 The free boson and Heisenberg algebras . 2.4 The free fermion and Cliford affinisation 2.5 The βγ system (ghost bosons) . . . . . .
5 Free fields realizations of irreductible highest weight modules of Lie algebras 5.1 The vertex operator realization in terms of free bosons . . . . 5.2 The Wakimoto realization in terms of free bosons and bosonic ghost pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Realizations in terms of free fermions . . . . . . . . . . . . . .
Bibliography [1] P. Etingof, I. B. Frenkel, and A. A. Kirillov. Lectures on representation theory and Knizhnik-Zamolodchikov equations, volume 58 of Mathematical Surveys and Monographs. American Mathematical Society, 1999. [2] P. Di Francesco, P. Mathieu, and D. S´en´echal. Conformal field theory. Graduate Texts in Contemporary Physics. Springer, 1996. [3] I. Frenkel, J. Lepowsky, and A. Meurman. Vertex operator algebras and the Monster, volume 134 of Pure and Applied Mathematics. Academic Press, Inc. [4] J. Fuchs. Affine Lie algebras and quantum groups. Cambridge Monographs on Mathematical Physics. Cambridge University Press, 1992. [5] V. Kac. Vertex algebras for beginners, volume 10 of University Lecture Series. American Mathematical Society, Providence, 1997.
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