Journal of Lie Theory

no. 3
Coadjoint Orbits for A+n-1, B+n, and D+n
Journal of Lie Theory, Volume 16 (2006) no. 3, pp. 455-469
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 $A_{n-1}^+$.
DOI: 10.5802/jolt.419
Classification: 17B30,17B35
Keywords: Coadjoint orbit, nilpotent Lie algebra 
@article{JOLT_2006_16_3_a2,
     author = {S. Mukherjee},
     title = {Coadjoint {Orbits} for {A\protect\textsuperscript{+}\protect\textsubscript{n-1},} {B\protect\textsuperscript{+}\protect\textsubscript{n},} and {D\protect\textsuperscript{+}\protect\textsubscript{n}}},
     journal = {Journal of Lie Theory},
     pages = {455--469},
     year = {2006},
     volume = {16},
     number = {3},
     doi = {10.5802/jolt.419},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.419/}
}
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%A S. Mukherjee
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S. Mukherjee. Coadjoint Orbits for A+n-1, B+n, and D+n. Journal of Lie Theory, Volume 16 (2006) no. 3, pp. 455-469. doi: 10.5802/jolt.419

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