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Moscow Mathematical Journal

Volume 13, Issue 2, April–June 2013  pp. 281–313.

Bernstein–Gelfand–Gelfand Reciprocity and Indecomposable Projective Modules for Classical Algebraic Supergroups

Authors Caroline Gruson (1) and Vera Serganova (2)
Author institution: (1) Université de Lorraine, U.M.R. 7502 du CNRS, Institut Elie Cartan, 54506 Vandoeuvre-les-Nancy Cedex, France
(2) Department of Mathematics, University of California, Berkeley, CA, 94720-3840 USA


We prove a BGG type reciprocity law for the category of finite dimensional modules over algebraic supergroups satisfying certain conditions. The equivalent of a standard module in this case is a virtual module called Euler characteristic due to its geometric interpretation. In the orthosymplectic case, we also describe indecomposable projective modules in terms of those Euler characteristics.

2010 Mathematics Subject Classification. 17B20.

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