Cellular subalgebras of the partition algebra
Representation Theory
2024-03-13 v2 Combinatorics
Rings and Algebras
Abstract
We describe various diagram algebras and their representation theory using cellular algebras of Graham and Lehrer and the decomposition into half diagrams. In particular, we show the diagram algebras surveyed here are all cellular algebras and parameterize their cell modules. We give a new construction to build new cellular algebras from a general cellular algebra and subalgebras of the rook Brauer algebra that we call the cellular wreath product.
Keywords
Cite
@article{arxiv.2211.08746,
title = {Cellular subalgebras of the partition algebra},
author = {Travis Scrimshaw},
journal= {arXiv preprint arXiv:2211.08746},
year = {2024}
}
Comments
43 pages, 4 tables; v2, added additional references, expanded proof of Theorem 3.2, other improvements