Timeline for References for Harish-Chandra pairs and modules, category "O"?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Mar 22, 2010 at 13:26 | comment | added | Jim Humphreys | Harish-Chandra modules have by now been studied extensively in a fairly algebraic context by Joseph (in many papers), Jantzen (especially in his enveloping algebra book, written in German), and many others. Even if your motivation comes from unitary representations of real Lie groups, as in work of Vogan and others, you are led to complexify the Lie algebras. The BGG category O theory illuminates mainly the complex Lie group part of the theory, but my book just tells the algebraic story leading up to the use of geometric/homological methods. This is already a long story. | |
| Dec 24, 2009 at 14:46 | comment | added | Leonid Positselski | Could you kindly say a couple of words about what Rosenberg does with Harish-Chandra modules in his book? The book itself unfortunately is not available for online view. | |
| Dec 24, 2009 at 11:52 | comment | added | Shizhuo Zhang | Yes, I just wanted to mention the book Enveloping algebras by Dixmer. Rosenberg's old book. "Noncommutative algebraic geometry and representation theory of quantized algebra" also contains the Harish-Chandra modules for one chapter. | |
| Nov 27, 2009 at 21:29 | history | edited | Leonid Positselski | CC BY-SA 2.5 |
The latter two paragraphs added.
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| Nov 27, 2009 at 17:33 | history | answered | Leonid Positselski | CC BY-SA 2.5 |