Foundations of Frobenius Heisenberg categories
Representation Theory
2023-09-29 v3 Category Theory
Abstract
We describe bases for the morphism spaces of the Frobenius Heisenberg categories associated to a symmetric graded Frobenius algebra, proving several open conjectures. Our proof uses a categorical comultiplication and generalized cyclotomic quotients of the category. We use our basis theorem to prove that the Grothendieck ring of the Karoubi envelope of the Frobenius Heisenberg category recovers the lattice Heisenberg algebra associated to the Frobenius algebra.
Keywords
Cite
@article{arxiv.2007.01642,
title = {Foundations of Frobenius Heisenberg categories},
author = {Jonathan Brundan and Alistair Savage and Ben Webster},
journal= {arXiv preprint arXiv:2007.01642},
year = {2023}
}
Comments
50 pages; v2: minor corrections, published version; v3: contains corrections of some errors present in the published version