Koszul duality for parabolic and singular category
Author:
Erik Backelin
Journal:
Represent. Theory 3 (1999), 139152
MSC (1991):
Primary 17B10, 18G15, 17B20
Published electronically:
July 19, 1999
MathSciNet review:
1703324
Fulltext PDF Free Access
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Abstract: This paper deals with a generalization of the ``Koszul duality theorem'' for the BernsteinGelfandGelfand category over a complex semisimple Liealgebra, established by Beilinson, Ginzburg and Soergel in Koszul duality patterns in representation theory, J. Amer. Math. Soc. 9 (1996), 473527. In that paper it was proved that any ``block'' in , determined by an integral, but possibly singular weight, is Koszul (i.e. equivalent to the category of finitely generated modules over some Koszul ring) and, moreover, that the ``Koszul dual'' of such a block is isomorphic to a ``parabolic subcategory'' of the trivial block in . We extend these results to prove that a parabolic subcategory of an integral and (possibly) singular block in is Koszul and we also calculate the Koszul dual of such a category.
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Additional Information
Erik Backelin
Affiliation:
Department of Mathematics, AlbertLudwigsUniversitat, Eckerstr. 1, D79104 Freiburg im Briesgau, Germany
Email:
erik@toto.mathematik.unifreiburg.de
DOI:
http://dx.doi.org/10.1090/S1088416599000552
PII:
S 10884165(99)000552
Received by editor(s):
August 24, 1998
Received by editor(s) in revised form:
January 31, 1999
Published electronically:
July 19, 1999
Article copyright:
© Copyright 1999
American Mathematical Society
