A new approach to the representation theory of the partition category
Representation Theory
2023-09-13 v1
Abstract
We explain a new approach to the representation theory of the partition category based on a reformulation of the definition of the Jucys-Murphy elements introduced originally by Halverson and Ram and developed further by Enyang. Our reformulation involves a new graphical monoidal category, the affine partition category, which is defined here as a certain monoidal subcategory of Khovanov's Heisenberg category. We use the Jucys-Murphy elements to construct some special projective functors, then apply these functors to give self-contained proofs of results of Comes and Ostrik on blocks of Deligne's category Rep(S_t).
Keywords
Cite
@article{arxiv.2107.05099,
title = {A new approach to the representation theory of the partition category},
author = {Jonathan Brundan and Max Vargas},
journal= {arXiv preprint arXiv:2107.05099},
year = {2023}
}