Cohomological Tensor Functors on Representations of the General Linear Supergroup

Download or read book Cohomological Tensor Functors on Representations of the General Linear Supergroup written by Thorsten Heidersdorf and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.