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
2018
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https://hal.archives-ouvertes.fr/hal-01470761
Contributeur : Arthur Soulié <>
Soumis le : mardi 6 novembre 2018 - 15:26:34
Dernière modification le : jeudi 8 novembre 2018 - 01:16:51

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LM1.pdf
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  • HAL Id : hal-01470761, version 5
  • ARXIV : 1702.08279

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Citation

Arthur Soulié. The Long-Moody construction and polynomial functors. 2018. 〈hal-01470761v5〉

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