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The Transition Matrix Between the Specht and ๐”ฐ๐”ฉ3 Web Bases is Unitriangular With Respect to Shadow Containment

The Transition Matrix Between the Specht and ๐”ฐ๐”ฉ3 Web Bases is Unitriangular With Respect to Shadow Containment

Abstract Webs are planar graphs with boundary that describe morphisms in a diagrammatic representation category for $\mathfrak{sl}_k$. They are studied extensively by knot theorists because braiding maps provide a categorical way to express link diagrams in terms of webs, producing quantum invariants like the well-known Jones polynomial. One important question โ€ฆ