Totally nonnegative Peterson variety and strongly dominant weight polytope
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918235922759680 |
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| author | Abe, Hiraku Gui, Tao Zeng, Haozhi |
| author_facet | Abe, Hiraku Gui, Tao Zeng, Haozhi |
| contents | We study the totally nonnegative part of the Peterson variety in arbitrary Lie type and establish its connection to the strongly dominant weight polytope. In particular, we prove that the totally nonnegative part of the Peterson variety is a regular CW-complex, which is homeomorphic to a cube as a cell-decomposed space. This confirms a conjecture of Rietsch for all Lie types. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06646 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Totally nonnegative Peterson variety and strongly dominant weight polytope Abe, Hiraku Gui, Tao Zeng, Haozhi Algebraic Geometry Combinatorics Representation Theory 14M15, 14M25, 05E14, 20G20, 15B48 We study the totally nonnegative part of the Peterson variety in arbitrary Lie type and establish its connection to the strongly dominant weight polytope. In particular, we prove that the totally nonnegative part of the Peterson variety is a regular CW-complex, which is homeomorphic to a cube as a cell-decomposed space. This confirms a conjecture of Rietsch for all Lie types. |
| title | Totally nonnegative Peterson variety and strongly dominant weight polytope |
| topic | Algebraic Geometry Combinatorics Representation Theory 14M15, 14M25, 05E14, 20G20, 15B48 |
| url | https://arxiv.org/abs/2512.06646 |