The Long-Moody construction and polynomial functors

Abstract : 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: it gives an endofunctor, called the Long-Moody functor, between the category of functors from the homogeneous category associated with the braid groupoid to a module category. Then we study the effect of the Long-Moody functor on strong polynomial functors: we prove that it increases by one the degree of strong polynomiality.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01470761
Contributeur : Arthur Soulié <>
Soumis le : mercredi 17 mai 2017 - 19:05:53
Dernière modification le : vendredi 19 mai 2017 - 01:01:36

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  • HAL Id : hal-01470761, version 2
  • ARXIV : 1702.08279

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Arthur Soulié. The Long-Moody construction and polynomial functors. 2017. <hal-01470761v2>

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