Schur Functors and Categorified Plethysm
Representation Theory
2023-07-04 v3 Category Theory
Abstract
It is known that the Grothendieck group of the category of Schur functors is the ring of symmetric functions. This ring has a rich structure, much of which is encapsulated in the fact that it is a "plethory": a monoid in the category of birings with its substitution monoidal structure. We show that similarly the category of Schur functors is a "2-plethory", which descends to give the plethory structure on symmetric functions. Thus, much of the structure of symmetric functions exists at a higher level in the category of Schur functors.
Cite
@article{arxiv.2106.00190,
title = {Schur Functors and Categorified Plethysm},
author = {John C. Baez and Joe Moeller and Todd Trimble},
journal= {arXiv preprint arXiv:2106.00190},
year = {2023}
}
Comments
53 pages