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	Non disponible
ISBN 13	9781470463267
ISBN 10	1470463261
Titre	Representations of Semisimple Lie Algebras in the BGG Category O
Auteur	James E Humphreys
Série	Graduate Studies In Mathematics
État	Non disponible
Type de reliure	Paperback
Éditeur	American Mathematical Society
Année de publication	2008-10-30
Nombre de pages	289
Note de couverture	La photo du livre est présentée à titre d'illustration uniquement. La reliure, la couverture ou l'édition réelle peuvent varier.
Note	Non disponible