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Selecta Mathematica

, 3:303 | Cite as

The Cohen-Macaulay property of the category of $ ({\frak g}, K) $-modules

  • J. Bernstein
  • A. Braverman
  • D. Gaitsgory
Article

Abstract.

Let \( ({\frak g}, K) \) be a Harish-Chandra pair. In this paper we prove that if P and P' are two projective \( ({\frak g}, K) \)-modules, then Hom(P, P') is a Cohen-Macaulay module over the algebra \( {\cal Z}({\frak g}, K) \) of K-invariant elements in the center of \( U({\frak g}) \). This fact implies that the category of \( ({\frak g}, K) \)-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.

Keywords

$ ({\frak g} K) $-modules Cohen-Macaulay categories Grothendieck duality. 

Copyright information

© Birkhäuser Verlag, Basel 1997

Authors and Affiliations

  • J. Bernstein
    • 1
  • A. Braverman
    • 1
  • D. Gaitsgory
    • 1
  1. 1.School of Mathematical SciencesTel-Aviv UniversityRamat-AvivIsrael

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