On invariants of representations of Weyl groups associated with the cohomology of toric varieties
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915821535625216 |
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| author | Gong, Tao |
| author_facet | Gong, Tao |
| contents | For a Weyl group $W$ and a $W$-permutohedron $P$, there are associated toric varieties $X_P$ and $X_{P/W_K}$ for any parabolic subgroup $W_K$ of $W$, since the quotient $P/W_K$ can be identified with a polytope inside $P$. We construct an explicit algebra isomorphism between $H^*(X_{P/W_K};\mathbb{Q})$ and $H^*(X_P;\mathbb{Q})^{W_K}$. We further generalize this isomorphism to intermediate lattices, to finite Coxeter groups, and to non-degenerate $W$-symmetric polytopes. Our results give affirmative answers to two open questions of Horiguchi--Masuda--Shareshain--Song. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_23631 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On invariants of representations of Weyl groups associated with the cohomology of toric varieties Gong, Tao Algebraic Topology Algebraic Geometry Representation Theory Primary 13A50, Secondary 14M25, 20F55, 52B20 For a Weyl group $W$ and a $W$-permutohedron $P$, there are associated toric varieties $X_P$ and $X_{P/W_K}$ for any parabolic subgroup $W_K$ of $W$, since the quotient $P/W_K$ can be identified with a polytope inside $P$. We construct an explicit algebra isomorphism between $H^*(X_{P/W_K};\mathbb{Q})$ and $H^*(X_P;\mathbb{Q})^{W_K}$. We further generalize this isomorphism to intermediate lattices, to finite Coxeter groups, and to non-degenerate $W$-symmetric polytopes. Our results give affirmative answers to two open questions of Horiguchi--Masuda--Shareshain--Song. |
| title | On invariants of representations of Weyl groups associated with the cohomology of toric varieties |
| topic | Algebraic Topology Algebraic Geometry Representation Theory Primary 13A50, Secondary 14M25, 20F55, 52B20 |
| url | https://arxiv.org/abs/2602.23631 |