Strongly dominant weight polytopes are cubes
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909190303252480 |
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| author | Burrull, Gaston Gui, Tao Hu, Hongsheng |
| author_facet | Burrull, Gaston Gui, Tao Hu, Hongsheng |
| contents | For any root system of rank $r$, we study the "dominant weight polytope" $P^λ$ associated with a strongly dominant weight $λ$. We prove that $P^λ$ is combinatorially equivalent to the $r$-dimensional cube. As an application, we give a new proof of the known formulas for Betti numbers of Peterson varieties in classical Lie types. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16022 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strongly dominant weight polytopes are cubes Burrull, Gaston Gui, Tao Hu, Hongsheng Representation Theory Combinatorics 05E10 (Primary), 52B05, 52B20, 14M25, 57S12 (Secondary) For any root system of rank $r$, we study the "dominant weight polytope" $P^λ$ associated with a strongly dominant weight $λ$. We prove that $P^λ$ is combinatorially equivalent to the $r$-dimensional cube. As an application, we give a new proof of the known formulas for Betti numbers of Peterson varieties in classical Lie types. |
| title | Strongly dominant weight polytopes are cubes |
| topic | Representation Theory Combinatorics 05E10 (Primary), 52B05, 52B20, 14M25, 57S12 (Secondary) |
| url | https://arxiv.org/abs/2311.16022 |