The Virasoro algebra is an infinite dimensional Lie algebra that
plays an increasingly important role in mathematics and theoretical
physics. This book describes some fundamental facts about the
representation theory of the Virasoro algebra in a self-contained
manner. Topics include the structure of Verma modules and Fock
modules, the classification of (unitarizable) Harish-Chandra
modules, tilting equivalence, and the rational vertex operator
algebras associated to the so-called minimal series
representations.
Covering a wide range of material, this book has three
appendices which provide background information required for some
of the chapters. The authors organize fundamental results in a
unified way and refine existing proofs. For instance in chapter
three, a generalization of Jantzen filtration is reformulated in an
algebraic manner, and geometric interpretation is provided.
Statements, widely believed to be true, are collated, and results
which are known but not verified are proven, such as the corrected
structure theorem of Fock modules in chapter eight.
This book will be of interest to a wide range of mathematicians
and physicists from the level of graduate students to
researchers.
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