A new Young wall realization of $B(λ)$ and $B(\infty)$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911800350474240 |
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| author | Fan, Zhaobing Han, Shaolong Kang, Seok-Jin Kim, Young Rock |
| author_facet | Fan, Zhaobing Han, Shaolong Kang, Seok-Jin Kim, Young Rock |
| contents | Using new combinatorics of Young walls, we give a new construction of the arbitrary level highest weight crystal $B(λ)$ for the quantum affine algebras of types $A^{(2)}_{2n}$, $D^{(2)}_{n+1}$, $A^{(2)}_{2n-1}$, $D^{(1)}_n$, $B^{(1)}_n$ and $C^{(1)}_n$. We show that the crystal consisting of reduced Young walls is isomorphic to the crystal $B(λ)$. Moreover, we provide a new realization of the crystal $B(\infty)$ in terms of reduced virtual Young walls and reduced extended Young walls. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11055 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new Young wall realization of $B(λ)$ and $B(\infty)$ Fan, Zhaobing Han, Shaolong Kang, Seok-Jin Kim, Young Rock Quantum Algebra Combinatorics Representation Theory Using new combinatorics of Young walls, we give a new construction of the arbitrary level highest weight crystal $B(λ)$ for the quantum affine algebras of types $A^{(2)}_{2n}$, $D^{(2)}_{n+1}$, $A^{(2)}_{2n-1}$, $D^{(1)}_n$, $B^{(1)}_n$ and $C^{(1)}_n$. We show that the crystal consisting of reduced Young walls is isomorphic to the crystal $B(λ)$. Moreover, we provide a new realization of the crystal $B(\infty)$ in terms of reduced virtual Young walls and reduced extended Young walls. |
| title | A new Young wall realization of $B(λ)$ and $B(\infty)$ |
| topic | Quantum Algebra Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2403.11055 |