The paper “Dual pairs for matrix groups“, co-authored by Paul Skerritt and  Cornelia Vizman (University of Timişoara, Romania) has been published in the Journal of Geometric Mechanics.  They present two dual pairs that can be seen as the linear analogues of the EPDiff dual pair due to Holm & Marsden, and the ideal fluid dual pair due to Marsden & Weinstein. A link to the published paper is here.