The Long–Moody construction and polynomial functors

Soulie, A. (2019) The Long–Moody construction and polynomial functors. Annales de l'Institut Fourier, 69(4), pp. 1799-1856. (doi: 10.5802/aif.3282)

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In 1994, Long and Moody gave a construction on representations of braid groups which associates a representation of Bn with a representation of Bn+1. In this paper, we prove that this construction is functorial and can be extended: it inspires endofunctors, called Long–Moody functors, on the category of functors from Quillen’s bracket construction associated with the braid groupoid to a module category. Then we study the effect of Long–Moody functors on strong polynomial functors: we prove that they increase by one the degree of very strong polynomiality.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Soulie, Dr Arthur
Authors: Soulie, A.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Annales de l'Institut Fourier
Publisher:Association des Annales de l'Institut Fourier
ISSN (Online):1777-5310
Copyright Holders:Copyright © 2019 Association des Annales de l’institut Fourier
First Published:First published in Annales de l'Institut Fourier 69(4):1799-1856
Publisher Policy:Reproduced under a Creative Commons License

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