Cohomological tensor functors on representations of the general linear supergroup

• Verfasst von: Heidersdorf, Thorsten [VerfasserIn]
• Verfasst von: Weissauer, Rainer [VerfasserIn]
• Titel: Cohomological tensor functors on representations of the general linear supergroup
• Verf.angabe: Thorsten Heidersdorf, Rainer Weissauer
• E-Jahr: 2021
• Jahr: June 23, 2021
• Umfang: 96 S.
• Teil: volume:270
• Teil: year:2021
• Teil: number:1320
• Teil: pages:1-96
• Teil: extent:96
• Fussnoten: Gesehen am 13.08.2021
• Titel Quelle: Enthalten in: Heidersdorf, ThorstenCohomological tensor functors on representations of the general linear supergroup
• Ort Quelle: Providence : American Mathematical Society, 2021
• Jahr Quelle: 2021
• Band/Heft Quelle: 270(2021), 1320, Seite 1-96
• ISBN Quelle: 978-1-4704-6528-5
• DOI: doi:10.1090/memo/1320
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: character formulas
• Sach-SW: highest weight categories
• Sach-SW: lie
• K10plus-PPN: 176677654X

Abstract

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.