2002/03/22 by J. M. Landsberg, Landsberg, J. M., Laurent Manivel +2
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.AG #math.DG #math.RT
paper · pdf · doi:10.48550/arxiv.math/0203241
21 pages
openalex publication_date 2002/03/22 · arxiv created 2002/12/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For various series of complex semi-simple Lie algebras \fg (t) equipped with irreducible representations V(t), we decompose the tensor powers of V(t) into irreducible factors in a uniform manner, using a tool we call \it diagram induction. In particular, we interpret the decompostion formulas of Deligne \citedel and Vogel \citevog for decomposing \fg\ot k respectively for the exceptional series and k≤ 4 and all simple Lie algebras and k≤ 3, as well as new formulas for the other rows of Freudenthal's magic chart. By working with Lie algebras augmented by the symmetry group of a marked Dynkin diagram, we are able to extend the list \citebrion of modules for which the algebra of invariant regular functions under a maximal nilpotent subalgebra is a polynomial algebra. Diagram induction applied to the exterior algebra furnishes new examples of distinct representations having the same Casimir eigenvalue.