Cohomological tensor functors on representations of the general linear supergroup - Heidersdorf, Thorsten; Weissauer, Rainer (Cohomological tensor functors on representations of the general linear supergroup, 2021)
We define and study cohomological tensor functors from the category T-n of finite-dimensional representations of the supergroup Gl(n vertical bar n) into Tn-r for 0 < r <= n. In the case DS : Tn -> Tn-1 we prove a formula DS(L) = circle plus Pi(ni) L-i for the image of an arbitrary irreducible representation. In particular DS(L) is semisimple and multiplicity free. We derive a few applications of this theorem such as the degeneration of certain spectral sequences and a formula for the modified superdimension of an irreducible representation.
Gesehen am 13.08.2021