Representation Theory – Current Trends and Perspectives

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pp: 331–373

DOI: 10.4171/171-1/13

Highest weight categories and strict polynomial functors. With an appendix by Cosima Aquilino

Henning Krause[1]

(1) Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501, Bielefeld, Germany

Highest weight categories are described in terms of standard objects and recollements of abelian categories, working over an arbitrary commutative base ring. Then the highest weight structure for categories of strict polynomial functors is explained, using the theory of Schur and Weyl functors. A consequence is the well-known fact that Schur algebras are quasi-hereditary.

Keywords: Highest weight category, strict polynomial functor, polynomial representation, divided power, Schur algebra, quasi-hereditary algebra, Ringel duality