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Rigid representations of a double quiver of type A , and Richardson elements in seaweed Lie algebras
Author(s) -
Jensen Bernt Tore,
Su Xiuping,
Yu Rupert Wei Tze
Publication year - 2009
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn087
Subject(s) - mathematics , quiver , lie algebra , quotient , type (biology) , nilpotent , pure mathematics , graded lie algebra , orbit (dynamics) , algebra over a field , adjoint representation , ecology , engineering , biology , aerospace engineering
In this paper, we show that there is always an open adjoint orbit in the nilpotent radical of a seaweed Lie algebra in gl n ( k ), thus answering positively in this gl n ( k ) case to a question raised independently by Michel Duflo and Dmitri Panyushev. The proof gives an explicit construction, using Δ‐filtered modules of quasi‐hereditary algebras arising from quotients of the double of quivers of type A . An example of a seaweed Lie algebra in a simple Lie algebra of type E 8 not admitting an open orbit in its nilpotent radical is given.