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Journal of Lie Theory 16 (2006), No. 3, 455--469
Copyright Heldermann Verlag 2006

Coadjoint Orbits for A+n-1, B+n, and D+n

Shantala Mukherjee
22 West Mayfield, Edinburgh EH9 1TQ, England


A complete description of the coadjoint orbits for $A_{n-1}^{+}$, the nilpotent Lie algebra of $n\times n$ strictly upper triangular matrices, has not yet been obtained, though there has been steady progress on it ever since the orbit method was devised. We apply methods developed by Andr\'{e} to find defining equations for the elementary coadjoint orbits for the maximal nilpotent Lie subalgebras of the orthogonal Lie algebras, and we also determine all the possible dimensions of coadjoint orbits in the case of $A_{n-1}^+$.

Keywords: Coadjoint orbit, nilpotent Lie algebra.

MSC: 17B30,17B35

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