English

Defining an Affine Partition Algebra

Representation Theory 2021-10-19 v1

Abstract

We define an affine partition algebra by generators and relations and prove a variety of basic results regarding this new algebra analogous to those of other affine diagram algebras. In particular we show that it extends the Schur-Weyl duality between the symmetric group and the partition algebra. We also relate it to the affine partition category recently defined by J. Brundan and M. Vargas. Moreover, we show that this affine partition category is a full monoidal subcategory of the Heisenberg category.

Keywords

Cite

@article{arxiv.2110.08652,
  title  = {Defining an Affine Partition Algebra},
  author = {Samuel Creedon and Maud De Visscher},
  journal= {arXiv preprint arXiv:2110.08652},
  year   = {2021}
}

Comments

47 pages

R2 v1 2026-06-24T06:56:46.202Z