Gröbner crystal structures
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_ | 1866916997888999424 |
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| author | Price, Abigail Stelzer, Ada Yong, Alexander |
| author_facet | Price, Abigail Stelzer, Ada Yong, Alexander |
| contents | We develop a theory of bicrystalline ideals, synthesizing Gröbner basis techniques and Kashiwara's crystal theory. This provides a unified algebraic, combinatorial, and computational approach that applies to ideals of interest, old and new. The theory concerns ideals in the coordinate ring of matrices, stable under the action of some Levi group, whose quotients admit standard bases equipped with a crystal structure. We construct an effective algorithm to decide if an ideal is bicrystalline. When the answer is affirmative, we provide a uniform, generalized Littlewood-Richardson rule for computing the multiplicity of irreducible representations either for the quotient or the ideal itself. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gröbner crystal structures Price, Abigail Stelzer, Ada Yong, Alexander Representation Theory Commutative Algebra Combinatorics We develop a theory of bicrystalline ideals, synthesizing Gröbner basis techniques and Kashiwara's crystal theory. This provides a unified algebraic, combinatorial, and computational approach that applies to ideals of interest, old and new. The theory concerns ideals in the coordinate ring of matrices, stable under the action of some Levi group, whose quotients admit standard bases equipped with a crystal structure. We construct an effective algorithm to decide if an ideal is bicrystalline. When the answer is affirmative, we provide a uniform, generalized Littlewood-Richardson rule for computing the multiplicity of irreducible representations either for the quotient or the ideal itself. |
| title | Gröbner crystal structures |
| topic | Representation Theory Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2510.07560 |