Cell 2-representations of finitary 2-categories
Representation Theory
2019-02-20 v1
Abstract
We study 2-representations of finitary 2-categories with involution and adjunctions by functors on module categories over finite dimensional algebras. In particular, we define, construct and describe in detail (right) cell 2-representations inspired by Kazhdan-Lusztig cell modules for Hecke algebras. Under some natural assumptions we show that cell 2-representations are strongly simple and do not depend on the choice of a right cell inside a two-sided cell. This reproves and extends the uniqueness result on categorification of Kazhdan-Lusztig cell modules for Hecke algebras of type from \cite{MS2}.
Cite
@article{arxiv.1011.3322,
title = {Cell 2-representations of finitary 2-categories},
author = {Volodymyr Mazorchuk and Vanessa Miemietz},
journal= {arXiv preprint arXiv:1011.3322},
year = {2019}
}
Comments
25 pages