The Long-Moody construction and polynomial functors

Arthur Soulié (1)

1 IRMA - Institut de Recherche Mathématique Avancée

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.

Mots clés: Burau representations; Functor categories; Braid groups; Long-Moody Construction

Domaines: Topologie algébrique [math.AT]; Catégories et ensembles [math.CT]

Arthur Soulié. The Long-Moody construction and polynomial functors. 2017. ⟨hal-01470761v2⟩