On the category of finite-dimensional representations of OSp: Part I

  • Michael Ehrig

    Universität Bonn, Germany
  • Catharina Stroppel

    Universität Bonn, Germany
On the category of finite-dimensional representations of OSp$(r|2n)$: Part I cover

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We study the combinatorics of the category of fi nite-dimensional modules for the orthosymplectic Lie supergroup OSp. In particular we present a positive counting formula for the dimension of the space of homomorphisms between two projective modules. This refines earlier results of Gruson and Serganova. For each block we construct an algebra whose module category shares the combinatorics with . It arises as a subquotient of a suitable limit of type D Khovanov algebras. It turns out that is isomorphic to the endomorphism algebra of a minimal projective generator of . This provides a direct link from to parabolic categories of type B/D, with maximal parabolic of type A, to the geometry of isotropic Grassmannians of types B/D and to Springer fibres of type C/D. We also indicate why is not highest weight in general.