Coadjoint orbits for A_n-1⁺, B_n⁺, and D_n⁺

2005/01/20 by Shantala Mukherjee, Mukherjee, Shantala
Mathematics · #17B30 #17B35 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.math/0501332

openalex publication_date 2005/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A complete description of the coadjoint orbits for A_n-1⁺, the nilpotent Lie algebra of n-by-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 Andre' 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⁺.

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