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Leonid Positselski
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The book "Enveloping algebras" by Dixmier appears to contain some material on Harish-Chandra modules in the classical sense (i.e., with respect to the maximal compact subgroup) and also on Verma modules, though not on Harish-Chandra pairs or category "O".

Besides, there is a new book "Representations of semisimple Lie algebras in the BGG category O", by Humphreys, AMS 2008. It discusses category O at great length and contains also some words about the classical Harish-Chandra modules. Abstract Harish-Chandra pairs aren't mentioned.

A discussion of algebraic Harish-Chandra pairs in the infinite-dimensional proalgebraic setting (over the complex numbers) can be found in the unpublished paper "Notes on Conformal Field Theory" by Beilinson-Feigin-Mazur.

The book "Enveloping algebras" by Dixmier appears to contain some material on Harish-Chandra modules in the classical sense (i.e., with respect to the maximal compact subgroup) and also on Verma modules, though not on Harish-Chandra pairs or category "O".

The book "Enveloping algebras" by Dixmier appears to contain some material on Harish-Chandra modules in the classical sense (i.e., with respect to the maximal compact subgroup) and also on Verma modules, though not on Harish-Chandra pairs or category "O".

Besides, there is a new book "Representations of semisimple Lie algebras in the BGG category O", by Humphreys, AMS 2008. It discusses category O at great length and contains also some words about the classical Harish-Chandra modules. Abstract Harish-Chandra pairs aren't mentioned.

A discussion of algebraic Harish-Chandra pairs in the infinite-dimensional proalgebraic setting (over the complex numbers) can be found in the unpublished paper "Notes on Conformal Field Theory" by Beilinson-Feigin-Mazur.

Source Link
Leonid Positselski
  • 15.6k
  • 1
  • 57
  • 95

The book "Enveloping algebras" by Dixmier appears to contain some material on Harish-Chandra modules in the classical sense (i.e., with respect to the maximal compact subgroup) and also on Verma modules, though not on Harish-Chandra pairs or category "O".