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

Joseph Bernstein, A. Braverman, D. Gaitsgory

• 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.