A partial order on bipartitions from the generalized Springer correspondence

  • Jianqiao Xia

    Massachusetts Institute of Technology, Cambridge, USA
A partial order on bipartitions from the generalized Springer correspondence cover
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Abstract

In [1], Lusztig gives an explicit formula for the bijection between the set of bipartitions and the set N\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 N\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