Nil-Brauer categorifies the split iquantum group of rank one
Quantum Algebra
2025-09-03 v2 Representation Theory
Abstract
We prove that the Grothendieck ring of the monoidal category of finitely generated graded projective modules for the nil-Brauer category is isomorphic to an integral form of the split iquantum group of rank one. Under this isomorphism, the indecomposable graded projective modules correspond to the icanonical basis. We also derive character formulae for irreducible graded modules and deduce various branching rules.
Keywords
Cite
@article{arxiv.2305.05877,
title = {Nil-Brauer categorifies the split iquantum group of rank one},
author = {Jonathan Brundan and Weiqiang Wang and Ben Webster},
journal= {arXiv preprint arXiv:2305.05877},
year = {2025}
}
Comments
Minor changes for consistency with our subsequent work 2505.22929