Koszul duality for parabolic

and singular category

Author:
Erik Backelin

Journal:
Represent. Theory **3** (1999), 139-152

MSC (1991):
Primary 17B10, 18G15, 17B20

DOI:
https://doi.org/10.1090/S1088-4165-99-00055-2

Published electronically:
July 19, 1999

MathSciNet review:
1703324

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper deals with a generalization of the ``Koszul duality theorem'' for the Bernstein-Gelfand-Gelfand category over a complex semi-simple Lie-algebra, established by Beilinson, Ginzburg and Soergel in *Koszul duality patterns in representation theory*, J. Amer. Math. Soc. 9 (1996), 473-527. 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, Albert-Ludwigs-Universitat, Eckerstr. 1, D-79104 Freiburg im Briesgau, Germany

Email:
erik@toto.mathematik.uni-freiburg.de

DOI:
https://doi.org/10.1090/S1088-4165-99-00055-2

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