Séminaires à venir

Parabolic induction for algebraic groups and stacks has many interesting applications in enumerative geometry and representation theory. One of them is that it can be used to construct various algebraic structures, including Ringel–Hall algebras, cohomological Hall algebras, Joyce vertex algebras, and so on, which are closely related to and sometimes motivated by enumerative problems, but at the same time, they themselves often are or are related to interesting quantum algebras, such as quantum groups. In this talk, I will explain how to view these constructions from a combinatorial viewpoint, as coming from the root datum of the general linear groups. This leads to natural generalizations to other algebraic groups, giving modules and other structures instead of algebras. Furthermore, I will introduce a generalization of root datum from algebraic groups to algebraic stacks, called the component lattice, and briefly discuss its combinatorial properties.