PreprintCC BY 4.0arXiv
Categorification in Representation Theory
Abstract
In this survey article, we give an introduction to the relatively young subject of $2$-representation theory, which studies categorifications of important players in classical representation theory. In particular, we provide a streamlined exposition of the main results leading to the classification of simple $2$-representations for Soergel bimodules associated to finite Weyl groups in characteristic $0$, obtained in [M. Mackaay, V. Mazorchuk, V. Miemietz, D. Tubbenhauer and X. Zhang, Simple transitive $2$-representations of Soergel bimodules for finite Coxeter types. Proc. London Math. Soc. 126 (2023)].
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BibTeX
@misc{miemietz2026categorification,
title = {{Categorification in Representation Theory}},
author = {Vanessa Miemietz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.19830},
eprint = {2608.19830},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.19830},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Categorification in Representation Theory
AU - Vanessa Miemietz
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2608.19830
UR - https://arxiv.org/abs/2608.19830
AB - In this survey article, we give an introduction to the relatively young subject of $2$-representation theory, which studies categorifications of important players in classical representation theory. In particular, we provide a streamlined exposition of the main results leading to the classification of simple $2$-representations for Soergel bimodules associated to finite Weyl groups in characteristic $0$, obtained in [M. Mackaay, V. Mazorchuk, V. Miemietz, D. Tubbenhauer and X. Zhang, Simple transitive $2$-representations of Soergel bimodules for finite Coxeter types. Proc. London Math. Soc. 126 (2023)].
ER -