University of Sydney Algebra Seminar

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 \(\mathfrak{sl}_2\), where they use singular blocks of category O for \(\mathfrak{sl}_m\) and translation functors. Here we construct a positive characteristic analogue using blocks of representations of \(\mathfrak{sl}_m\) 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.