Algebra Seminar: Nandakumar -- Categorification via blocks of modular representations in type A

Vinoth Nandakumar (University of Sydney) 

Friday 26 August, 12-1pm, Place: Carslaw 375 

Categorification via blocks of modular representations in type A 

Bernstein-Frenkel-Khovanov have constructed a categorification of tensor products of the
standard representation of sl_2, where they use singular blocks of category O for sl_m
and translation functors.  Here we construct a positive characteristic analogue using
blocks of representations of sl_m in positive characteristic, with 0 Frobenius
character, and singular Harish-Chandra character.  We also show that this it admits a
graded lift, which is equivalent to a geometric categorification constructed by Cautis,
Kamnitzer and Licata using coherent sheaves on co-tangent bundles to Grassmanians (after
applying equivalences due to Riche and Bezrukavnikov-Mirkovic-Rumynin).  This is joint
work with Gufang Zhao.