Monday, September 9, 2019 - 4:30pm
UC Riverside / Dartmouth
The category O of Bernstein-Gelfand-Gelfand and the Schur algebra are interesting and fundamental objects. Following motivation connected to 3-dimensional supersymmetric gauge theory, Braden-Licata-Proudfoot-Webster defined an analogue of category O associated to any hypertoric (aka toric hyperkahler) variety. In joint work with Braden, we use the same geometry to define analogues of the Schur algebra. In fact, we are able to define such an algebra starting from any matroid. In work in progress with Ethan Kowalenko, we extend the construction of Braden-Licata-Proudfoot-Webster to a matroidal setting as well. In work in progress with Jens Eberhardt, we show that these matroidal Schur algebras and matroidal category O are related to each other via a categorification.