Grading of affine Weyl semi-groups of Kac-Moody type
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912150151233536 |
|---|---|
| author | Philippe, Paul |
| author_facet | Philippe, Paul |
| contents | For any Kac-Moody root data $\mathcal D$, D. Muthiah and D. Orr have defined a partial order on the semi-direct product $W^+$ of the integral Tits cone with the vectorial Weyl group of $\mathcal D$, and a strictly compatible $\mathbb Z$-valued length function. We classify covers for this order and show that this length function defines a $\mathbb Z$-grading of $W^+$, generalizing the case of affine ADE root systems and giving a positive answer to a conjecture of Muthiah and Orr. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_04514 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Grading of affine Weyl semi-groups of Kac-Moody type Philippe, Paul Representation Theory Combinatorics 20F55 (20G44 20C08 22E67) For any Kac-Moody root data $\mathcal D$, D. Muthiah and D. Orr have defined a partial order on the semi-direct product $W^+$ of the integral Tits cone with the vectorial Weyl group of $\mathcal D$, and a strictly compatible $\mathbb Z$-valued length function. We classify covers for this order and show that this length function defines a $\mathbb Z$-grading of $W^+$, generalizing the case of affine ADE root systems and giving a positive answer to a conjecture of Muthiah and Orr. |
| title | Grading of affine Weyl semi-groups of Kac-Moody type |
| topic | Representation Theory Combinatorics 20F55 (20G44 20C08 22E67) |
| url | https://arxiv.org/abs/2306.04514 |