A Partial Order on Bipartitions From the Generalized Springer Correspondence
Representation Theory
2018-10-24 v3
Abstract
In \cite{Lusztig}, Lusztig gives an explicit formula for the bijection between the set of bipartitions and the set of unipotent classes in a spin group which carry irreducible local systems equivariant for the spin group but not equivariant for the special orthogonal group. The set has a natural partial order and therefore induces a partial order on bipartitions. We use the explicit formula given in \cite{Lusztig} to prove that this partial order on bipartitions is the same as the dominance order appeared in Dipper-James-Murphy's work.
Cite
@article{arxiv.1801.09599,
title = {A Partial Order on Bipartitions From the Generalized Springer Correspondence},
author = {Jianqiao Xia},
journal= {arXiv preprint arXiv:1801.09599},
year = {2018}
}