Twin masures associated with Kac-Moody groups over Laurent polynomials
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917898845421568 |
|---|---|
| author | Bardy-Panse, Nicole Hebert, Auguste Rousseau, Guy |
| author_facet | Bardy-Panse, Nicole Hebert, Auguste Rousseau, Guy |
| contents | Let $\mathfrak{G}$ be a split reductive group, $\mathbb{k}$ be a field and $\varpi$ be an indeterminate. In order to study $\mathfrak{G}(\mathbb{k}[\varpi,\varpi^{-1}])$ and $\mathfrak{G}(\mathbb{k}(\varpi))$, one can make them act on their twin building $\mathcal{I} = \mathcal{I}_\oplus\times \mathcal{I}_\ominus$, where $\mathcal{I}_\oplus$ and $\mathcal{I}_\ominus$ are related via a ''codistance''. Masures are generalizations of Bruhat-Tits buildings adapted to the study of Kac-Moody groups over valued fields. Motivated by the work of Dinakar Muthiah on Kazhdan-Lusztig polynomials associated with Kac-Moody groups, we study the action of $\mathfrak{G}(\mathbb{k}[\varpi,\varpi^{-1}])$ and $\mathfrak{G}(\mathbb{k}(\varpi,\varpi^{-1}))$ on their ''twin masure'', when $\mathfrak{G}$ is a split Kac-Moody group instead of a reductive group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_07603 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Twin masures associated with Kac-Moody groups over Laurent polynomials Bardy-Panse, Nicole Hebert, Auguste Rousseau, Guy Group Theory Representation Theory Let $\mathfrak{G}$ be a split reductive group, $\mathbb{k}$ be a field and $\varpi$ be an indeterminate. In order to study $\mathfrak{G}(\mathbb{k}[\varpi,\varpi^{-1}])$ and $\mathfrak{G}(\mathbb{k}(\varpi))$, one can make them act on their twin building $\mathcal{I} = \mathcal{I}_\oplus\times \mathcal{I}_\ominus$, where $\mathcal{I}_\oplus$ and $\mathcal{I}_\ominus$ are related via a ''codistance''. Masures are generalizations of Bruhat-Tits buildings adapted to the study of Kac-Moody groups over valued fields. Motivated by the work of Dinakar Muthiah on Kazhdan-Lusztig polynomials associated with Kac-Moody groups, we study the action of $\mathfrak{G}(\mathbb{k}[\varpi,\varpi^{-1}])$ and $\mathfrak{G}(\mathbb{k}(\varpi,\varpi^{-1}))$ on their ''twin masure'', when $\mathfrak{G}$ is a split Kac-Moody group instead of a reductive group. |
| title | Twin masures associated with Kac-Moody groups over Laurent polynomials |
| topic | Group Theory Representation Theory |
| url | https://arxiv.org/abs/2210.07603 |