Generalizing Lusztig's total positivity
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917651834470400 |
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| author | Guichard, Olivier Wienhard, Anna |
| author_facet | Guichard, Olivier Wienhard, Anna |
| contents | We introduce the notion of $Θ$-positivity in real simple Lie groups. This notion at the same time generalizes Lusztig's total positivity in split real Lie groups and invariant orders in Lie groups of Hermitian type. We show that there are four families of Lie groups which admit $Θ$-positive structures, and investigate basic properties of $Θ$-positivity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_10114 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Generalizing Lusztig's total positivity Guichard, Olivier Wienhard, Anna Differential Geometry Group Theory We introduce the notion of $Θ$-positivity in real simple Lie groups. This notion at the same time generalizes Lusztig's total positivity in split real Lie groups and invariant orders in Lie groups of Hermitian type. We show that there are four families of Lie groups which admit $Θ$-positive structures, and investigate basic properties of $Θ$-positivity. |
| title | Generalizing Lusztig's total positivity |
| topic | Differential Geometry Group Theory |
| url | https://arxiv.org/abs/2208.10114 |