English

Categorified quantum sl(2) is an inverse limit of flag 2-categories

Quantum Algebra 2014-03-18 v2

Abstract

We prove that categorified quantum sl(2) is an inverse limit of Flag 2-categories defined using cohomology rings of iterated flag varieties. This inverse limit is an instance of a 2-limit in a bicategory giving rise to a universal property that characterizes the categorification of quantum sl(2) uniquely up to equivalence. As an application we characterize all bimodule homomorphisms in the Flag 2-category and prove that the categorified quantum Casimir of sl(2) acts appropriately on these 2-representations.

Keywords

Cite

@article{arxiv.1205.3608,
  title  = {Categorified quantum sl(2) is an inverse limit of flag 2-categories},
  author = {Anna Beliakova and Aaron D. Lauda},
  journal= {arXiv preprint arXiv:1205.3608},
  year   = {2014}
}

Comments

21 pages, with xypic diagrams. v2 corrects typos