The Long-Moody construction and polynomial functors
Soulié, Arthur
HAL, hal-01470761 / Harvested from HAL
Text on HAL
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.
Publié le : 2018-11-06
Classification:  Functor categories,  Burau representations,  Long-Moody Construction,  Braid groups,  [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT],  [MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT] 
@article{hal-01470761,
     author = {Souli\'e, Arthur},
     title = {The Long-Moody construction and polynomial functors},
     journal = {HAL},
     volume = {2018},
     number = {0},
     year = {2018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01470761}
}

Soulié, Arthur. The Long-Moody construction and polynomial functors. HAL, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/hal-01470761/