An invariant of links in a handlebody associated with the spin 𝑗 representation of 𝑈_{𝑞}(𝔰𝔩(2,𝐂))

Nakabo, Shigekazu

doi:10.1090/S0002-9939-1993-1132416-9

An invariant of links in a handlebody associated with the spin $j$ representation of $U_ q(\mathfrak {sl}(2, \mathbf {C}))$
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Proc. Amer. Math. Soc. 118 (1993), 645-655 Request permission

Abstract:

We construct an invariant of framed links in a handlebody by means of the spin $j$ representation of ${U_q}(\mathfrak {s}\mathfrak {l}(2,\mathbb {C}))$. We can see this invariant is an extension of the Jones polynomial and Kauffman’s Dubrovnik polynomial. Moreover, we can obtain a linear representation of the generalized braid group associated with the Lie algebras of types $B$ and $C$ by applying the operators used in constructing an invariant to tangles in a solid torus.

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