Rigid representations of a double quiver of type A, and Richardson elements in seaweed Lie algebras

Bernt T Jensen, Xiuping Su, Rupert Wei Tze Yu

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4 Citations (Scopus)

Abstract

In this paper, we show that there is always an open adjoint orbit in the nilpotent radical of a seaweed Lie algebra in gln(k), thus answering positively in this gln(k) case to a question raised independently by Michel Duflo and Dmitri Panyushev. The proof gives an explicit construction, using �-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 E8 not admitting an open orbit in its nilpotent radical is given.
Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalBulletin of the London Mathematical Society
Volume41
Issue number1
Early online date26 Nov 2008
DOIs
Publication statusPublished - Feb 2009

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Quiver
Lie Algebra
Orbit
Quasi-hereditary Algebra
Simple Lie Algebra
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Rigid representations of a double quiver of type A, and Richardson elements in seaweed Lie algebras. / Jensen, Bernt T; Su, Xiuping; Yu, Rupert Wei Tze.

In: Bulletin of the London Mathematical Society, Vol. 41, No. 1, 02.2009, p. 1-15.

Research output: Contribution to journalArticle

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