Algebra Seminar: Nandakumar -- Modular representations of sl_n with two-row nilpotent p-character

Vinoth Nandakumar (University of Sydney) 

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

Title: Modular representations of sl_n with two-row nilpotent p-character 

Abstract: 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.