Bernstein-Gel'fand-Gel'fand reciprocity and indecomposable projective modules for classical algebraic supergroups

Caroline Gruson (1) , Vera Serganova (2)

1 IECL - Institut Élie Cartan de Lorraine
2 LBNL - Lawrence Berkeley National Laboratory [Berkeley]

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.

Keywords: Finite dimensional representations of algebraic supergroups; BGG reciprocity law; Flag variety

Domains: Representation Theory [math.RT]

Caroline Gruson, Vera Serganova. Bernstein-Gel'fand-Gel'fand reciprocity and indecomposable projective modules for classical algebraic supergroups. Moscow Mathematical Journal, 2013, 13 (2), pp.281-313. ⟨10.1007/978-1-4471-4863-0_7⟩. ⟨hal-01093230⟩