Representations of the exceptional and other Lie algebras with integral eigenvalues of the Casimir operator
| dc.creator | Macfarlane, A. J. | |
| dc.creator | Pfeiffer, Hendryk | |
| dc.date | 2002-08-08 | |
| dc.date | 2003-01-13 | |
| dc.date.accessioned | 2026-07-07T07:56:14Z | |
| dc.date.available | 2026-07-07T07:56:14Z | |
| dc.description | The uniformity, for the family of exceptional Lie algebras g, of the decompositions of the powers of their adjoint representations is well-known now for powers up to the fourth. The paper describes an extension of this uniformity for the totally antisymmetrised n-th powers up to n=9, identifying (see Tables 3 and 6) families of representations with integer eigenvalues 5,...,9 for the quadratic Casimir operator, in each case providing a formula (see eq. (11) to (15)) for the dimensions of the representations in the family as a function of D=dim g. This generalises previous results for powers j and Casimir eigenvalues j, j<=4. Many intriguing, perhaps puzzling, features of the dimension formulas are discussed and the possibility that they may be valid for a wider class of not necessarily simple Lie algebras is considered. | |
| dc.description | 16 pages, LaTeX, 1 figure, 9 tables; v2: presentation improved, typos corrected | |
| dc.identifier | https://arxiv.org/abs/math-ph/0208014 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0208014 | |
| dc.identifier | J. Phys. A: Math. Gen. 36 (2003) 2305-2317 | |
| dc.identifier | doi:10.1088/0305-4470/36/9/308 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127236 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Representation Theory | |
| dc.subject | 17B10 (Primary), 17B25 (Secondary) | |
| dc.title | Representations of the exceptional and other Lie algebras with integral eigenvalues of the Casimir operator | |
| dc.type | text |