Quasi-admissible, raisable nilpotent orbits and covering Barbasch-Vogan duality
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911693779501056 |
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| author | Zhang, Yi-Yang |
| author_facet | Zhang, Yi-Yang |
| contents | For simply-connected Lie groups of type E over \( p \)-adic local field \( F \), we determine the degree of the cover required for a given \( F \)-split nilpotent orbit to be quasi-admissible or raisable, respectively. Combining this result with the previously computed data for other types by Gao-Liu-Tsai, we prove that all \( F \)-split nilpotent orbits whose geometry type contained in the image of the covering Barbasch-Vogan duality map \( d_{\mathrm{BV},G}^{(n)} \) of almost-simple Lie groups \( G \) in each Cartan type are always\( \overline{G}^{(n)} \)-quasi-admissible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17901 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasi-admissible, raisable nilpotent orbits and covering Barbasch-Vogan duality Zhang, Yi-Yang Representation Theory For simply-connected Lie groups of type E over \( p \)-adic local field \( F \), we determine the degree of the cover required for a given \( F \)-split nilpotent orbit to be quasi-admissible or raisable, respectively. Combining this result with the previously computed data for other types by Gao-Liu-Tsai, we prove that all \( F \)-split nilpotent orbits whose geometry type contained in the image of the covering Barbasch-Vogan duality map \( d_{\mathrm{BV},G}^{(n)} \) of almost-simple Lie groups \( G \) in each Cartan type are always\( \overline{G}^{(n)} \)-quasi-admissible. |
| title | Quasi-admissible, raisable nilpotent orbits and covering Barbasch-Vogan duality |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2605.17901 |