Poset polytopes and pipe dreams: types C and B
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916865400373248 |
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| author | Makedonskyi, Ievgen Makhlin, Igor |
| author_facet | Makedonskyi, Ievgen Makhlin, Igor |
| contents | The first part of this paper concerns type C. We present new explicitly defined families of algebro-combinatorial structures of three kinds: combinatorial bases in representations, Newton--Okounkov bodies of flag varieties and toric degenerations of flag varieties. All three families are parametrized by the same family of polytopes: the marked chain-order polytopes of Fang and Fourier which interpolate between the type C Gelfand--Tsetlin and FFLV polytopes. Thus, in each case the obtained structures interpolate between the well-known bases, Newton--Okounkov bodies or degenerations associated with the latter two polytopes. We then obtain similar results for type B after introducing a new family of poset polytopes to be considered in place of marked chain-order polytopes. In both types our constructions and proofs rely crucially on a combinatorial connection between poset polytopes and pipe dreams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16207 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Poset polytopes and pipe dreams: types C and B Makedonskyi, Ievgen Makhlin, Igor Representation Theory Algebraic Geometry Combinatorics The first part of this paper concerns type C. We present new explicitly defined families of algebro-combinatorial structures of three kinds: combinatorial bases in representations, Newton--Okounkov bodies of flag varieties and toric degenerations of flag varieties. All three families are parametrized by the same family of polytopes: the marked chain-order polytopes of Fang and Fourier which interpolate between the type C Gelfand--Tsetlin and FFLV polytopes. Thus, in each case the obtained structures interpolate between the well-known bases, Newton--Okounkov bodies or degenerations associated with the latter two polytopes. We then obtain similar results for type B after introducing a new family of poset polytopes to be considered in place of marked chain-order polytopes. In both types our constructions and proofs rely crucially on a combinatorial connection between poset polytopes and pipe dreams. |
| title | Poset polytopes and pipe dreams: types C and B |
| topic | Representation Theory Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2402.16207 |