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 -