In , 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  to prove that this partial order on bipartitions is the same as the dominance order appeared in Dipper–James–Murphy's work .
Cite this article
Jianqiao Xia, A partial order on bipartitions from the generalized Springer correspondence. J. Comb. Algebra 2 (2018), no. 3, pp. 301–309DOI 10.4171/JCA/2-3-4