Cohomological Tensor Functors on Representations of the General Linear Supergroup

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Thorsten Heidersdorf, Rainer Weissauer
English | 2021 | ISBN: 1470447142 | 118 Pages | True PDF | 1.25 MB

We define and study cohomological tensor functors from the category Tn of finite-dimensional representations of the supergroup Gl(n|n) into Tn−r for 0 < r ≤ n. In the case DS : Tn → Tn−1 we prove a formula DS(L) = ΠniLi 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.


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