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E-BooksCohomological Tensor Functors on Representations of the General Linear Supergroup



Cohomological Tensor Functors on Representations of the General Linear Supergroup
Free Download Cohomological Tensor Functors on Representations of the General Linear Supergroup
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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