Clasped web bases from hourglass plabic graphs
Pranav Enugandla, Christian Gaetz

TL;DR
This paper extends the web basis construction from $U_q(rak{sl}_3)$ to $U_q(rak{sl}_4)$ using hourglass plabic graphs, providing combinatorial characterizations and establishing basis properties for tensor invariants.
Contribution
It introduces combinatorial characterizations of basis webs in the kernel of projection maps for $U_q(rak{sl}_4)$ tensor invariants, generalizing previous work for $U_q(rak{sl}_3)$.
Findings
Basis webs form a basis for tensor invariants.
Provides combinatorial criteria for basis webs.
Establishes clasped web bases for tensor products.
Abstract
G.-Pechenik-Pfannerer-Striker-Swanson applied hourglass plabic graphs to construct web bases for spaces of tensor invariants of fundamental representations of , extending Kuperberg's celebrated basis for . We give several combinatorial characterizations of basis webs in the kernel of the projection to invariants in a tensor product of arbitrary (type ) 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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Taxonomy
TopicsFinite Group Theory Research · Advanced Combinatorial Mathematics · Algebraic structures and combinatorial models
