Representations of Semisimple Lie Algebras in the BGG Category O Humphreys

Representations of Semisimple Lie Algebras in the BGG Category OAuthor(s): James E Humphreys\nFormat: Paperback\nPublisher: American Mathematical Society, United States\nImprint: American Mathematical Society\nISBN-13: 9781470463267, 978-1470463267\nSynopsis\nThis is the first textbook treatment of work leading to the landmark 1979 Kazhdan Lusztig Conjecture on characters of simple highest weight modules for a semisimple Lie algebra g over C. The setting is the module category O introduced by BernsteinGelfandGelfand, which includes all highest weight modules for g such as Verma modules and finite dimensional simple modules. Analogues of this category have become influential in many areas of representation theory.\n\nPart I can be used as a text for independent study or for a mid-level one semester graduate course; it includes exercises and examples. The main prerequisite is familiarity with the structure theory of g. Basic techniques in category O such as BGG Reciprocity and Jantzens.