Series of Lie Groups
| dc.creator | Landsberg, J. M. | |
| dc.creator | Manivel, L. | |
| dc.date | 2002-03-22 | |
| dc.date | 2002-12-20 | |
| dc.date.accessioned | 2026-07-07T04:47:15Z | |
| dc.date.available | 2026-07-07T04:47:15Z | |
| dc.description | 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 $k\leq 4$ and all simple Lie algebras and $k\leq 3$, 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. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0203241 | |
| dc.identifier | http://arxiv.org/abs/math/0203241 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63640 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | Representation Theory | |
| dc.title | Series of Lie Groups | |
| dc.type | text |