Titlebook: Representation Theory of the Virasoro Algebra; Kenji Iohara,Yoshiyuki Koga Book 2011 Springer-Verlag London Limited 2011 Fock modules.Hari

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Fock Modules,ingular vectors of Fock modules in terms of Jack symmetric polynomials, and ii) the relation between semi-infinite forms and the bosonic Fock modules. This chapter uses some results from Chapters 5 and 6.

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Preliminary,ropriate to work within the framework of what we call .-graded Lie algebras. Hence, we also present a categorical setup for representations of .-graded Lie algebras and some of their properties such as local composition series, (co)homologies, and Berstein-Gelfand-Gelfand duality.

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Classification of Harish-Chandra Modules,module, a lowest weight module, or the module of type ..ℂ[.,..](.).. The proof is given by the reduction to positive characteristic cases. Hence, for the reader who is not familiar with Lie .-algebras and their representations, we make a brief survey of the general theory of Lie .-algebras in Append

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The Jantzen Filtration, effective tool to analyze Verma modules over these algebras. Here, we present the Jantzen filtration and explain some of their properties. We also generalise this filtration to analyze Fock modules over Vir in Chapter 8. The generalisation given here first appeared in this book.

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Determinant Formulae,l role when we analyze the Verma modules in Chapters 5 and 6. The determinant formulae of the Vir-module maps from a Verma module to the Fock module (with the same highest weight) and from a Fock module to the contragredient dual of the Verma module (with the same highest weight) play an important r

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Verma Modules II: Structure Theorem, of Verma modules is completely determined from which the Bernstein−Gelfand−Gelfand type resolution follows. As a simple corollary, the characters of the all irreducible highest weight modules over Vir are given. In particular, the characters of minimal series representations, with fixed central cha

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