Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2507.16968 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913955384918016 |
|---|---|
| author | Gan, Wee Teck Gurevich, Nadya |
| author_facet | Gan, Wee Teck Gurevich, Nadya |
| contents | We consider the minimal representation of the adjoint split group $E_7$ over a p-adic field. The representation has a model in a space of functions on a 17 dimensional cone $Ω$, and elements of the unique parabolic subgroup Q with abelian radical act by simple geometric formulas. We write a formula for the action of an involutive element $s$, conjugating $Q$ to the opposite parabolic $\bar Q$. The resulting integral operator, called a Fourier transform on $Ω$, is related to generalized Fourier transform, defined by Braverman and Kazhdan. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16968 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fourier Transform and the minimal representation of $E_7$ Gan, Wee Teck Gurevich, Nadya Representation Theory 22E50 We consider the minimal representation of the adjoint split group $E_7$ over a p-adic field. The representation has a model in a space of functions on a 17 dimensional cone $Ω$, and elements of the unique parabolic subgroup Q with abelian radical act by simple geometric formulas. We write a formula for the action of an involutive element $s$, conjugating $Q$ to the opposite parabolic $\bar Q$. The resulting integral operator, called a Fourier transform on $Ω$, is related to generalized Fourier transform, defined by Braverman and Kazhdan. |
| title | Fourier Transform and the minimal representation of $E_7$ |
| topic | Representation Theory 22E50 |
| url | https://arxiv.org/abs/2507.16968 |