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

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arxiv 1111.6959 v1 pith:SEAZTTJI submitted 2011-11-29 math.RT

Caroline Gruson , Vera Serganova This is my paper · ORCID
classification math.RT
keywords modulesalgebraiccaseeulerindecomposablemoduleprojectivereciprocity
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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.

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  1. The highest weight theory for Representations of General Linear groups in the Verlinde categories in positive characteristic

    math.RT 2025-01 conditional novelty 6.0 of 10

    The paper proves that changing the Borel subgroup for GL(X) in Ver_p is governed by lowest weights of GL(L_m|L_n), computed via circular weight and cap diagrams.

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