University of Sydney Algebra Seminar

Vinoth Nandakumar (University of Sydney)

Friday 3 November, 12-1pm, Place: Carslaw 375

Modular representations of \(\mathfrak{sl}_n\) with two-row nilpotent \(p\)-character

We will study the category of modular representations of the special linear Lie algebra with a central p-character given by a nilpotent whose Jordan type is a two-row partition. Building on work of Cautis and Kamnitzer, we construct a categorification of the affine tangle calculus using these categories; the main technical tool is a geometric localization-type result of Bezrukavnikov, Mirkovic and Rumynin. Using this, we give combinatorial dimension formulae for the irreducible modules, composition multiplicities of the simples in the baby Vermas, and a description of the Ext spaces. This Ext algebra is an "annular" analogues of Khovanov’s arc algebra, and can be used to give an extension of Khovanov homology to links in the annulus. This is joint with Rina Anno and David Yang.