Ebook: Representations of contragredient Lie algebras and the Kac-Macdonald identities

Institute of Solid State Physics, Chernogolovka Institute of Earth Physics, Moscow. - 1982, - P. 25-77, English.
Preface.
The aim of this paper is to give an introducton to the theory of contragredient Lie algebras and their representations, following lines of the lecture of Bernstein and Gelfand.
The text is written for beginners, so we tried to make it as self-contained as possible (we begin with the definition of a Lie algebra!).
The reader is assumed to be familiar only with standard facts from linear algebra and some basic terminology from the theory of associative rings and modules over them.Content.
Introduction.
The Setting.
The Category O and Verma Modules.
Representations of sl2.
The Invariant Form and the Casimir Operator for Contragredient Lie Algebras.
Locally Finite Modules and their Characters.
Specializations of the Denominator Formula and Kac-Macdonald Identities.
Review of Some Recent Results Related to Contragredient Lie Algebras.
Bibliography (49 Books).