2014/09/03 by Li, Ge
#FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1409.1195
We construct a naturally \mathbb Z-graded algebra \mathscr Gn(δ) over R with KLR-like relations and give an explicit isomorphism between \mathscr Gn(δ) and \mathscr Bn(δ), the Brauer algebras over R, when R is a field of characteristic 0. This isomorphism allows us to exhibit a non-trivial \mathbb Z-grading on the Brauer algebras over a field of characteristic 0. As a byproduct of the proof, we also construct an explicit homogeneous cellular basis for \mathscr Gn(δ).