The Cohen-Macaulay property of the category of (g, K)-modules

Joseph Bernstein, Alexander Braverman, Dennis Gaitsgory

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


Let (g, K) be a Harish-Chandra pair. In this paper we prove that if P and P′ are two projective (g, K)-modules, then Hom(P, P′) is a Cohen-Macaulay module over the algebra Z(g, K) of K-invariant elements in the center of U(g). This fact implies that the category of (g, K)-modules is locally equivalent to the category of modules over a Cohen-Macaulay algebra, where by a Cohen-Macaulay algebra we mean an associative algebra that is a free finitely generated module over a polynomial subalgebra of its center.

Original languageEnglish
Pages (from-to)303-314
Number of pages12
JournalSelecta Mathematica, New Series
Issue number3
Publication statusPublished - 1997
Externally publishedYes


  • (g, K)-modules
  • Cohen-Macaulay categories
  • Grothendieck duality


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