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arXiv · 2512.08817

Clasped web bases from hourglass plabic graphs

Pranav Enugandla·Christian Gaetz
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Abstract

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.

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Pranav Enugandla, Christian Gaetz. 2025-12-09. Clasped web bases from hourglass plabic graphs. https://arxiv.org/abs/2512.08817

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