Abstract
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 supercharacters. 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.
Citation
Crystal Hoyt. Shifra Reif. "Grothendieck rings for Lie superalgebras and the Duflo–Serganova functor." Algebra Number Theory 12 (9) 2167 - 2184, 2018. https://doi.org/10.2140/ant.2018.12.2167
Information