Brent Everitt (University of York)

Friday 17th November, 12.05-12.55pm, Carslaw 373

Partial mirror symmetry

If by "mirror symmetry" one means the theory of reflection groups, then by "partial mirror symmetry" we mean the theory of reflection monoids. These are inverse monoids of partial linear isomorphisms of a vector space, and are defined using two pieces of data: a reflection group W and a collection of domain subspaces that form a W-invariant semi-lattice. Thus they encode situations where local symmetries are considered as well as global ones. The talk will outline the basic properties and examples, as well as connections with the theory of Renner monoids (which play the same role for affine algebraic monoids that the Weyl groups do for affine algebraic groups) and the theory of hyperplane arrangements.