English

Actions of sl_2 on algebras appearing in categorification

Representation Theory 2023-11-30 v2

Abstract

We prove that many of the recently-constructed algebras and categories which appear in categorification can be equipped with an action of sl2\mathfrak{sl}_2 by derivations. The sl2\mathfrak{sl}_2 representations which appear are filtered by tensor products of coverma modules. In a future paper, we will address the implications of the sl2\mathfrak{sl}_2 structure for categorification.

Keywords

Cite

@article{arxiv.2103.00048,
  title  = {Actions of sl_2 on algebras appearing in categorification},
  author = {Ben Elias and You Qi},
  journal= {arXiv preprint arXiv:2103.00048},
  year   = {2023}
}

Comments

50 pages, many figures. V2 contains updates from referee reports. Comments welcome. To appear in Quantum Topology