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

• J. Bernstein ^[1] ; A. Braverman ^[1] ; D. Gaitsgory ^[1]
  1. [1] Tel-Aviv University, Israel
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 3, Nº. 3, 1997, págs. 303-314
• Idioma: inglés
• DOI: 10.1007/s000290050012
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• Resumen

  • 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.