Young wall realizations of level 1 irreducible highest weight and Fock space crystals of quantum affine algebras in type E
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911779232153600 |
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| author | Laurie, Duncan |
| author_facet | Laurie, Duncan |
| contents | We construct Young wall models for the crystal bases of level $1$ irreducible highest weight representations and Fock space representations of quantum affine algebras in types $E_{6}^{(1)}$, $E_{7}^{(1)}$ and $E_{8}^{(1)}$. In each case, Young walls consist of coloured blocks stacked inside the relevant Young wall pattern which satisfy a certain combinatorial condition. Moreover the crystal structure is described entirely in terms of adding and removing blocks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03905 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Young wall realizations of level 1 irreducible highest weight and Fock space crystals of quantum affine algebras in type E Laurie, Duncan Representation Theory Quantum Algebra 05E10, 17B37, 20G42 We construct Young wall models for the crystal bases of level $1$ irreducible highest weight representations and Fock space representations of quantum affine algebras in types $E_{6}^{(1)}$, $E_{7}^{(1)}$ and $E_{8}^{(1)}$. In each case, Young walls consist of coloured blocks stacked inside the relevant Young wall pattern which satisfy a certain combinatorial condition. Moreover the crystal structure is described entirely in terms of adding and removing blocks. |
| title | Young wall realizations of level 1 irreducible highest weight and Fock space crystals of quantum affine algebras in type E |
| topic | Representation Theory Quantum Algebra 05E10, 17B37, 20G42 |
| url | https://arxiv.org/abs/2311.03905 |