Crystal Hoyt, Shifra Reif
Published 2016-12-17Version 1
We show that the Duflo-Serganova functor on the category of finite-dimensional modules over a finite-dimensional contragredient Lie superalgebra induces a ring homomorphism on a natural quotient of the Grothendieck ring, which is isomorphic to the ring of characters. We realize this homomorphism as a certain evaluation of functions related to the supersymmetry property. We use this realization to describe the kernel and image of the homomorphism induced by the Duflo-Serganova functor.
A few remarks on symmetries of the Duflo-Serganova functor
An Explicit Presentation of the Grothendieck Ring of Finitely Generated F_{q}[SL(2,F_{q})]-Modules
A note on the Grothendieck ring of the symmetric group
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