The Long-Moody construction and polynomial functors
Algebraic Topology
2021-08-17 v6 Category Theory
Abstract
In 1994, Long and Moody gave a construction on representations of braid groups which associates a representation of \mathbf{B}\_{n} with a representation of \mathbf{B}\_{n+1}. In this paper, we prove that this construction is functorial and can be extended: it inspires endofunctors, called Long-Moody functors, between 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.
Cite
@article{arxiv.1702.08279,
title = {The Long-Moody construction and polynomial functors},
author = {Arthur Souli{é}},
journal= {arXiv preprint arXiv:1702.08279},
year = {2021}
}