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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2512.08817 |
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| _version_ | 1866918239888474112 |
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| author | Enugandla, Pranav Gaetz, Christian |
| author_facet | Enugandla, Pranav Gaetz, Christian |
| contents | G.-Pechenik-Pfannerer-Striker-Swanson applied hourglass plabic graphs to construct web bases for spaces of tensor invariants of fundamental representations of $U_q(\mathfrak{sl}_4)$, extending Kuperberg's celebrated basis for $U_q(\mathfrak{sl}_3)$. We give several combinatorial characterizations of basis webs in the kernel of the projection to invariants in a tensor product of arbitrary (type $1$) irreducibles. We apply this to show that the nonzero images of basis webs form a basis (a property shared with Lusztig's dual canonical basis) yielding distinguished clasped web bases for each such tensor product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08817 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Clasped web bases from hourglass plabic graphs Enugandla, Pranav Gaetz, Christian Combinatorics Representation Theory G.-Pechenik-Pfannerer-Striker-Swanson applied hourglass plabic graphs to construct web bases for spaces of tensor invariants of fundamental representations of $U_q(\mathfrak{sl}_4)$, extending Kuperberg's celebrated basis for $U_q(\mathfrak{sl}_3)$. We give several combinatorial characterizations of basis webs in the kernel of the projection to invariants in a tensor product of arbitrary (type $1$) irreducibles. We apply this to show that the nonzero images of basis webs form a basis (a property shared with Lusztig's dual canonical basis) yielding distinguished clasped web bases for each such tensor product. |
| title | Clasped web bases from hourglass plabic graphs |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2512.08817 |