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Koszul, Ringel and Serre duality for strict polynomial functors

Part of: Linear algebraic groups and related topics Abelian categories Homological algebra Categories with structure

Published online by Cambridge University Press:  18 March 2013

Henning Krause
Henning Krause*
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld, Germany email [email protected]
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Abstract

This is a report on recent work of Chałupnik and Touzé. We explain the Koszul duality for the category of strict polynomial functors and make explicit the underlying monoidal structure which seems to be of independent interest. Then we connect this to Ringel duality for Schur algebras and describe Serre duality for strict polynomial functors.

Keywords

strict polynomial functorpolynomial representationSchur algebradivided powerKoszul dualityRingel dualitySerre duality

MSC classification

Secondary: 20G05: Representation theory 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories 18E30: Derived categories, triangulated categories 18G10: Resolutions; derived functors 20G10: Cohomology theory 20G43: Schur and $q$-Schur algebras
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 6 , June 2013 , pp. 996 - 1018
Copyright
© The Author(s) 2013 

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