Representations of Semisimple Lie Algebras in the BGG Category O by James E Humphreys

Representations of Semisimple Lie Algebras in the BGG Category O by James E Humphreys

This 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 Bernstein–Gelfand–Gelfand, 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. Part 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 Jantzen’s translation functors are developed, culminating in an overview of the proof of the Kazhdan–Lusztig Conjecture (due to Beilinson–Bernstein and Brylinski–Kashiwara). The full proof however is beyond the scope of this book, requiring deep geometric methods: D -modules and perverse sheaves on the flag variety. Part II introduces closely related topics important in current research: parabolic category O , projective functors, tilting modules, twisting and completion functors, and Koszul duality theorem of Beilinson–Ginzburg–Soergel.

James E. Humphreys, University of Massachusetts, Amherst, MA

SKU	Unavailable
ISBN 13	9781470463267
ISBN 10	1470463261
Title	Representations of Semisimple Lie Algebras in the BGG Category O
Author	James E Humphreys
Series	Graduate Studies In Mathematics
Condition	Unavailable
Binding Type	Paperback
Publisher	American Mathematical Society
Year published	2008-10-30
Number of pages	289
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note	Unavailable