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Applied Categorical Structures

, Volume 26, Issue 2, pp 287–308 | Cite as

Operations on Categories of Modules are Given by Schur Functors

  • Martin BrandenburgEmail author
Article
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Abstract

Let k be a commutative \(\mathbb {Q}\)-algebra. We study families of functors between categories of finitely generated modules which are defined for all commutative k-algebras simultaneously and are compatible with base changes. These operations turn out to be Schur functors associated to k-linear representations of symmetric groups. This result is closely related to Macdonald’s classification of polynomial functors.

Keywords

Polynomial functor Schur functor Base change Module categories 

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Notes

Acknowledgements

I am very grateful to Alexandru Chirvasitu, who made major contributions to this paper in its early stages, particularly to Sect. 4. I also would like to thank Ingo Blechschmidt for sharing his beautiful constructive proofs appearing in Sect. 6, Oskar Braun for his careful proofreading of the preprint, Bernhard Köck for drawing my attention to [18], as well as Antoine Touzé and Ivo Dell’Ambrogio for helpful discussions on the subject at the University of Lille. Finally I would like to thank the anonymous referee for making several suggestions for improvement.

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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.MünsterGermany

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