2018年4月6日 16時30分 ～ 2018年4月6日 18時00分
We can consider the Long-Moody construction from a functorial point of view: I will show that it defines an endofunctor, called a Long-Moody functor, on a suitable category associated with braid groups. Moreover, we will see that we can modify this construction so as to recover more representations of braid groups. Also, I will present the generalisations of the Long-Moody functor for other families of groups, such as mapping class groups of orientable and non-orientable surfaces or mapping class groups of 3-manifolds.
Then, I will present the remarkable effect of a Long-Moody functor on polynomial functors: it increases by one the degree of weak and very strong polynomiality. Thus, the Long-Moody constructions provides new examples of twisted coefficients corresponding to the framework developed by Randal-Williams and Wahl.