Categorified quantum sl(2) and equivariant cohomology of iterated flag varieties

TL;DR

This paper constructs a new representation of a categorified quantum sl(2) using equivariant cohomology of iterated flag varieties, providing a categorification of the (N+1)-dimensional irreducible representation.

Contribution

It introduces a novel geometric construction of a categorified quantum sl(2) representation via equivariant cohomology of iterated flag varieties.

Findings

Provides a geometric model for the categorified quantum sl(2) representation.

Categorifies the (N+1)-dimensional irreducible quantum sl(2) representation.

Connects categorification with equivariant cohomology and flag varieties.

Abstract

A 2-category was introduced in arXiv:0803.3652 [math.QA] that categorifies Lusztig's integral version of quantum sl(2). Here we construct for each positive integer N arepresentation of this 2-category using the equivariant cohomology of iterated flag varieties. This representation categorifies the irreducible (N+1)-dimensional representation of quantum sl(2).