| | |
| | |
Stat |
Members: 3643 Articles: 2'488'730 Articles rated: 2609
29 March 2024 |
|
| | | |
|
Article overview
| |
|
Fundamental Weights, Permutation Weights and Weyl Character Formula | Hasan R. Karadayi
; Meltem Gungormez
; | Date: |
19 Jun 1998 | Journal: | J.Phys. A32 (1999) 1701-1707 | Subject: | Mathematical Physics; Representation Theory; Group Theory | math-ph hep-th math.GR math.MP math.RT | Abstract: | For a finite Lie algebra $G_N$ of rank N, the Weyl orbits $W(Lambda^{++})$ of strictly dominant weights $Lambda^{++}$ contain $dimW(G_N)$ number of weights where $dimW(G_N)$ is the dimension of its Weyl group $W(G_N)$. For any $W(Lambda^{++})$, there is a very peculiar subset $wp(Lambda^{++})$ for which we always have $$ dimwp(Lambda^{++})=dimW(G_N)/dimW(A_{N-1}) . $$ For any dominant weight $ Lambda^+ $, the elements of $wp(Lambda^+)$ are called {f Permutation Weights}. It is shown that there is a one-to-one correspondence between elements of $wp(Lambda^{++})$ and $wp(
ho)$ where $
ho$ 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 $Lambda^+$, calculation of the character $ChR(Lambda^+)$ for irreducible representation $R(Lambda^+)$ 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 {f Fundamental Weights} with which we obtain a quite relevant specialization in applications of Weyl character formula. | Source: | arXiv, math-ph/9806014 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |