Elementary construction of canonical bases, foldings, and piecewise linear bijections
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917899298406400 |
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| author | Shoji, Toshiaki Zhou, Zhiping |
| author_facet | Shoji, Toshiaki Zhou, Zhiping |
| contents | Let ${\mathbf U}_q^-$ be the negative half of a quantum group of finite type. We construct the canonical basis of ${\mathbf U}_q^-$ by applying the folding theory of quantum groups, and piecewise linear parametrization of canonical basis. Our construction is elementary, in the sense that we don't appeal to Lusztig's geometric theory of canonical bases, nor to Kashiwara's theory of crystal bases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12568 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elementary construction of canonical bases, foldings, and piecewise linear bijections Shoji, Toshiaki Zhou, Zhiping Quantum Algebra 17B37, 81R50 Let ${\mathbf U}_q^-$ be the negative half of a quantum group of finite type. We construct the canonical basis of ${\mathbf U}_q^-$ by applying the folding theory of quantum groups, and piecewise linear parametrization of canonical basis. Our construction is elementary, in the sense that we don't appeal to Lusztig's geometric theory of canonical bases, nor to Kashiwara's theory of crystal bases. |
| title | Elementary construction of canonical bases, foldings, and piecewise linear bijections |
| topic | Quantum Algebra 17B37, 81R50 |
| url | https://arxiv.org/abs/2501.12568 |