Dual canonical bases and embeddings of symmetric spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915412344569856 |
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| author | Bao, Huanchen Song, Jinfeng |
| author_facet | Bao, Huanchen Song, Jinfeng |
| contents | For a connected reductive group $G_k$ over an algebraically closed field $k$ of char $\neq 2$ and a fixed point subgroup $K_k$ under an algebraic group involution, we construct a quantization and an integral model of any affine embeddings of the symmetric space $G_k/K_k$. We show that the coordinate ring of any affine embedding of $G_k/K_k$ admits a dual canonical basis.
We further construct an integral model for the canonical embedding (that is, an embedding which is complete, simple, and toroidal) of $G_k/K_k$. When $G_k$ is of adjoint type, we obtain an integral model for the wonderful compactification of the symmetric space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01173 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dual canonical bases and embeddings of symmetric spaces Bao, Huanchen Song, Jinfeng Representation Theory Algebraic Geometry Quantum Algebra For a connected reductive group $G_k$ over an algebraically closed field $k$ of char $\neq 2$ and a fixed point subgroup $K_k$ under an algebraic group involution, we construct a quantization and an integral model of any affine embeddings of the symmetric space $G_k/K_k$. We show that the coordinate ring of any affine embedding of $G_k/K_k$ admits a dual canonical basis. We further construct an integral model for the canonical embedding (that is, an embedding which is complete, simple, and toroidal) of $G_k/K_k$. When $G_k$ is of adjoint type, we obtain an integral model for the wonderful compactification of the symmetric space. |
| title | Dual canonical bases and embeddings of symmetric spaces |
| topic | Representation Theory Algebraic Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2505.01173 |