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• W3049012064 abstract "Unitary fusion categories (UFCs) have gained increased attention due to emerging connections with quantum physics. We consider a fusion rule of the form $qotimes q cong mathbf{1}oplusbigoplus^k_{i=1}x_{i}$ in a UFC $mathcal{C}$, and extract information using the graphical calculus. For instance, we classify all associated skein relations when $k=1,2$ and $mathcal{C}$ is ribbon. In particular, we also consider the instances where $q$ is antisymmetrically self-dual. Our main results follow from considering the action of a rotation operator on a canonical basis. Assuming self-duality of the summands $x_{i}$, some general observations are made e.g. the real-symmetricity of the $F$-matrix $F^{qqq}_q$. We then find explicit formulae for $F^{qqq}_q$ when $k=2$ and $mathcal{C}$ is ribbon, and see that the spectrum of the rotation operator distinguishes between the Kauffman and Dubrovnik polynomials." @default.
• W3049012064 created "2020-08-21" @default.
• W3049012064 creator A5002944671 @default.
• W3049012064 creator A5063169316 @default.
• W3049012064 date "2020-08-17" @default.
• W3049012064 modified "2023-09-27" @default.
• W3049012064 title "Skein-Theoretic Methods for Unitary Fusion Categories" @default.
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• W3049012064 hasPublicationYear "2020" @default.
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