Representations of Semisimple Lie Algebras in the BGG Category O (0821846787)

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 $\mathfrak{g}$ over $\mathbb {C}$. The setting is the module category $\mathscr {O}$ introduced by Bernstein-Gelfand-Gelfand, which includes all highest weight modules for $\mathfrak{g}$ 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 $\mathfrak{g}$. Basic techniques in category $\mathscr {O}$ 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 $\mathscr {O}$, projective functors, tilting modules, twisting and completion functors, and Koszul duality theorem of Beilinson-Ginzburg-Soergel.

Product details

• Format Hardback | 289 pages
• Dimensions 184.15 x 260.35 x 25.4mm | 707.6g
• Publication date 17 Aug 2008
• Publisher American Mathematical Society
• Publication City/Country Providence, United States
• Language English
• Edition Statement UK ed.
• Illustrations note Illustrations
• ISBN10 0821846787
• ISBN13 9780821846780
• Bestsellers rank 1,533,084

Download Representations of Semisimple Lie Algebras in the BGG Category O (0821846787).pdf, available at secure.drbook.co for free.


or
DOWNLOAD