On the $U_{q}(osp(1|2n))$ and $U_{-q}(so(2n+1))$ Uncoloured Quantum Link Invariants

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dc.creatorBlumen, Sacha C.
dc.date2009-01-21
dc.date.accessioned2026-07-07T12:32:32Z
dc.date.available2026-07-07T12:32:32Z
dc.descriptionLet $L$ be a link and $Φ^{A}_{L}(q)$ its link invariant associated with the vector representation of the quantum (super)algebra $U_{q}(A)$. Let $F_{L}(r,s)$ be the Kauffman link invariant for $L$ associated with the Birman--Wenzl--Murakami algebra $BWM_{f}(r,s)$ for complex parameters $r$ and $s$ and a sufficiently large rank $f$. For an arbitrary link $L$, we show that $Φ^{osp(1|2n)}_{L}(q) = F_{L}(-q^{2n},q)$ and $Φ^{so(2n+1)}_{L}(-q) = F_{L}(q^{2n},-q)$ for each positive integer $n$ and all sufficiently large $f$, and that $Φ^{osp(1|2n)}_{L}(q)$ and $Φ^{so(2n+1)}_{L}(-q)$ are identical up to a substitution of variables. For at least one class of links $F_{L}(-r,-s) = F_{L}(r,s)$ implying $Φ^{osp(1|2n)}_{L}(q) = Φ^{so(2n+1)}_{L}(-q)$ for these links.
dc.description16 pages, 4 figures, accepted for publication by the Journal of Knot Theory and its Ramifications
dc.identifierhttps://arxiv.org/abs/0901.3232
dc.identifierhttp://arxiv.org/abs/0901.3232
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216811
dc.subjectQuantum Algebra
dc.subjectGeometric Topology
dc.subject57M27; 17B37
dc.titleOn the $U_{q}(osp(1|2n))$ and $U_{-q}(so(2n+1))$ Uncoloured Quantum Link Invariants
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