TY - JOUR

T1 - The Cohen-Macaulay property of the category of (g, K)-modules

AU - Bernstein, Joseph

AU - Braverman, Alexander

AU - Gaitsgory, Dennis

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

KW - (g, K)-modules

KW - Cohen-Macaulay categories

KW - Grothendieck duality

UR - http://www.scopus.com/inward/record.url?scp=0000427531&partnerID=8YFLogxK

U2 - 10.1007/s000290050012

DO - 10.1007/s000290050012

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AN - SCOPUS:0000427531

SN - 1022-1824

VL - 3

SP - 303

EP - 314

JO - Selecta Mathematica, New Series

JF - Selecta Mathematica, New Series

IS - 3

ER -