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- W2006009404 abstract "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 cite{del} and Vogel cite{vog} for decomposing $fg^{ot k}$ respectively for the exceptional series and $kleq 4$ and all simple Lie algebras and $kleq 3$, 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 cite{brion} 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." @default.
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- W2006009404 date "2004-08-01" @default.
- W2006009404 modified "2023-10-14" @default.
- W2006009404 title "Series of Lie groups" @default.
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- W2006009404 doi "https://doi.org/10.1307/mmj/1091112085" @default.
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