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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.14302 |
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| _version_ | 1866912935234764800 |
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| author | Jia, Boming |
| author_facet | Jia, Boming |
| contents | We compute the Hilbert series of the coordinate ring of some highest weight varieties. We also explain why Narayana numbers (and their generalizations) appear naturally in the numerator of the Hilbert series of the homogeneous coordinate ring of the Grassmannian $Gr(d,n+d+1)$ and of the minimal nilpotent adjoint orbit in $\mathfrak{sl}_\mathrm{n+1}(\mathbb{C})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14302 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Highest Weight Varieties and Narayana Numbers Jia, Boming Representation Theory Combinatorics 17B08, 17B10, 05E10 We compute the Hilbert series of the coordinate ring of some highest weight varieties. We also explain why Narayana numbers (and their generalizations) appear naturally in the numerator of the Hilbert series of the homogeneous coordinate ring of the Grassmannian $Gr(d,n+d+1)$ and of the minimal nilpotent adjoint orbit in $\mathfrak{sl}_\mathrm{n+1}(\mathbb{C})$. |
| title | Highest Weight Varieties and Narayana Numbers |
| topic | Representation Theory Combinatorics 17B08, 17B10, 05E10 |
| url | https://arxiv.org/abs/2310.14302 |