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

2011/11/29 by Caroline Gruson, Gruson, Caroline, Vera Serganova +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1111.6959

arxiv created 2011/11/29 · openalex publication_date 2011/11/29 · arxiv updated 2011/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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