# A partial order on bipartitions from the generalized Springer correspondence

### Jianqiao Xia

Massachusetts Institute of Technology, Cambridge, USA

## Abstract

In [1], Lusztig gives an explicit formula for the bijection between the set of bipartitions and the set $\mathcal{N}$ 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 $\mathcal{N}$ has a natural partial order and therefore induces a partial order on bipartitions. We use the explicit formula given in [1] to prove that this partial order on bipartitions is the same as the dominance order appeared in Dipper–James–Murphy's work [2].

## Cite this article

Jianqiao Xia, A partial order on bipartitions from the generalized Springer correspondence. J. Comb. Algebra 2 (2018), no. 3, pp. 301–309

DOI 10.4171/JCA/2-3-4