Fundamental Weights, Permutation Weights and Weyl Character Formula
| dc.creator | Karadayi, Hasan R. | |
| dc.creator | Gungormez, Meltem | |
| dc.date | 1998-06-19 | |
| dc.date | 1998-12-11 | |
| dc.date.accessioned | 2026-07-07T10:54:13Z | |
| dc.date.available | 2026-07-07T10:54:13Z | |
| dc.description | For a finite Lie algebra $G_N$ of rank N, the Weyl orbits $W(Λ^{++})$ of strictly dominant weights $Λ^{++}$ contain $dimW(G_N)$ number of weights where $dimW(G_N)$ is the dimension of its Weyl group $W(G_N)$. For any $W(Λ^{++})$, there is a very peculiar subset $\wp(Λ^{++})$ for which we always have $$ dim\wp(Λ^{++})=dimW(G_N)/dimW(A_{N-1}) . $$ For any dominant weight $ Λ^+ $, the elements of $\wp(Λ^+)$ are called {\bf Permutation Weights}. It is shown that there is a one-to-one correspondence between elements of $\wp(Λ^{++})$ and $\wp(ρ)$ where $ρ$ is the Weyl vector of $G_N$. The concept of signature factor which enters in Weyl character formula can be relaxed in such a way that signatures are preserved under this one-to-one correspondence in the sense that corresponding permutation weights have the same signature. Once the permutation weights and their signatures are specified for a dominant $Λ^+$, calculation of the character $ChR(Λ^+)$ for irreducible representation $R(Λ^+)$ will then be provided by $A_N$ multiplicity rules governing generalized Schur functions. The main idea is again to express everything in terms of the so-called {\bf Fundamental Weights} with which we obtain a quite relevant specialization in applications of Weyl character formula. | |
| dc.description | 6 pages, no figures, TeX, as will appear in Journal of Physics A:Mathematical and General | |
| dc.identifier | https://arxiv.org/abs/math-ph/9806014 | |
| dc.identifier | http://arxiv.org/abs/math-ph/9806014 | |
| dc.identifier | J.Phys.A32:1701-1707,1999 | |
| dc.identifier | doi:10.1088/0305-4470/32/9/016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/185738 | |
| dc.subject | Mathematical Physics | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Group Theory | |
| dc.subject | Representation Theory | |
| dc.title | Fundamental Weights, Permutation Weights and Weyl Character Formula | |
| dc.type | text |