Lie Theory Relative to a Hyperplane Arrangement
Wednesday, October 19, 2022
3:00 PM-4:00 PM
Dinner will follow the discussion with Professor Aguiar.
Abstract: A result due to Joyal, Klyachko, and Stanley relates free Lie algebras to partition lattices. We will discuss the precise relationship and interpret the result in terms of the braid hyperplane arrangement.
We will then extend this result to arbitrary (finite, real, and central) hyperplane arrangements, and do the same with several additional aspects of classical Hopf-Lie theory. The Tits monoid of an arrangement, and the notion of lune, play central roles in the discussion. All from joint work with Swapneel Mahajan.