Affine type A geometric crystal structure on the Grassmannian
We construct a type A(1) n−1 affine geometric crystal structure on the Grassmannian Gr(k, n). The tropicalization of this structure recovers the combinatorics of crystal operators on semistandard Young tableaux of rectangular shape (with n − k rows), including the affine crystal operator e 0. In par...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2020-04-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/6393/pdf |
| _version_ | 1797270227574063104 |
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| author | Gabriel Frieden |
| author_facet | Gabriel Frieden |
| author_sort | Gabriel Frieden |
| collection | DOAJ |
| description | We construct a type A(1) n−1 affine geometric crystal structure on the Grassmannian Gr(k, n). The tropicalization of this structure recovers the combinatorics of crystal operators on semistandard Young tableaux of rectangular shape (with n − k rows), including the affine crystal operator e 0. In particular, the promotion operation on these tableaux essentially corresponds to cyclically shifting the Plu ̈cker coordinates of the Grassmannian. |
| first_indexed | 2024-04-25T02:00:55Z |
| format | Article |
| id | doaj.art-b0134f03469e40c5adfd949cafc79ab9 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:55Z |
| publishDate | 2020-04-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-b0134f03469e40c5adfd949cafc79ab92024-03-07T14:55:20ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502020-04-01DMTCS Proceedings, 28th...10.46298/dmtcs.63936393Affine type A geometric crystal structure on the GrassmannianGabriel Frieden0Department of Mathematics [Ann Arbor]We construct a type A(1) n−1 affine geometric crystal structure on the Grassmannian Gr(k, n). The tropicalization of this structure recovers the combinatorics of crystal operators on semistandard Young tableaux of rectangular shape (with n − k rows), including the affine crystal operator e 0. In particular, the promotion operation on these tableaux essentially corresponds to cyclically shifting the Plu ̈cker coordinates of the Grassmannian.https://dmtcs.episciences.org/6393/pdf[math.math-co]mathematics [math]/combinatorics [math.co] |
| spellingShingle | Gabriel Frieden Affine type A geometric crystal structure on the Grassmannian Discrete Mathematics & Theoretical Computer Science [math.math-co]mathematics [math]/combinatorics [math.co] |
| title | Affine type A geometric crystal structure on the Grassmannian |
| title_full | Affine type A geometric crystal structure on the Grassmannian |
| title_fullStr | Affine type A geometric crystal structure on the Grassmannian |
| title_full_unstemmed | Affine type A geometric crystal structure on the Grassmannian |
| title_short | Affine type A geometric crystal structure on the Grassmannian |
| title_sort | affine type a geometric crystal structure on the grassmannian |
| topic | [math.math-co]mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/6393/pdf |
| work_keys_str_mv | AT gabrielfrieden affinetypeageometriccrystalstructureonthegrassmannian |