Rigid representations of a double quiver of type A, and Richardson elements in seaweed Lie algebras |
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Authors: | Jensen Bernt Tore; Su Xiuping; Yu Rupert Wei Tze |
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Institution: | Department of Mathematical Sciences Norwegian University of Science and Technology N-7034 Trondheim Norway berntj@math.ntnu.no |
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Abstract: | In this paper, we show that there is always an open adjointorbit in the nilpotent radical of a seaweed Lie algebra in gln(k),thus answering positively in this gln(k) case to a questionraised independently by Michel Duflo and Dmitri Panyushev. Theproof gives an explicit construction, using -filtered modulesof quasi-hereditary algebras arising from quotients of the doubleof quivers of type A. An example of a seaweed Lie algebra ina simple Lie algebra of type E8 not admitting an open orbitin its nilpotent radical is given. |
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