On combinatorics of string polytopes in types $B$ and $C$
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| Format: | Preprint |
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2023
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| _version_ | 1866910788613046272 |
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| author | Cho, Yunhyung Fujita, Naoki Lee, Eunjeong |
| author_facet | Cho, Yunhyung Fujita, Naoki Lee, Eunjeong |
| contents | A string polytope is a rational convex polytope whose lattice points parametrize a highest weight crystal basis, which is obtained from a string cone by explicit affine inequalities depending on a highest weight. It also inherits geometric information of a flag variety such as toric degenerations, Newton-Okounkov bodies, mirror symmetry, Schubert calculus, and so on. In this paper, we study combinatorial properties of string polytopes in types $B$ and $C$ by giving an explicit description of string cones in these types which is analogous to Gleizer-Postnikov's description of string cones in type $A$. As an application, we characterize string polytopes in type $C$ which are unimodularly equivalent to the Gelfand-Tsetlin polytope in type $C$ for a specific highest weight. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_11242 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On combinatorics of string polytopes in types $B$ and $C$ Cho, Yunhyung Fujita, Naoki Lee, Eunjeong Combinatorics Algebraic Geometry Representation Theory Primary: 05E10, secondary: 05A05, 14M15, 52B20 A string polytope is a rational convex polytope whose lattice points parametrize a highest weight crystal basis, which is obtained from a string cone by explicit affine inequalities depending on a highest weight. It also inherits geometric information of a flag variety such as toric degenerations, Newton-Okounkov bodies, mirror symmetry, Schubert calculus, and so on. In this paper, we study combinatorial properties of string polytopes in types $B$ and $C$ by giving an explicit description of string cones in these types which is analogous to Gleizer-Postnikov's description of string cones in type $A$. As an application, we characterize string polytopes in type $C$ which are unimodularly equivalent to the Gelfand-Tsetlin polytope in type $C$ for a specific highest weight. |
| title | On combinatorics of string polytopes in types $B$ and $C$ |
| topic | Combinatorics Algebraic Geometry Representation Theory Primary: 05E10, secondary: 05A05, 14M15, 52B20 |
| url | https://arxiv.org/abs/2306.11242 |