Paper submitted to J. Knot Theory and Its Ramifications

Tonight I submitted the following paper: paper.pdf to the Journal of Knot Theory and Its Ramifications – the paper hasn’t been refereed yet so I’m merely offering it here for the reader’s enjoyment.

ON THE UNCOLOURED QUANTUM LINK INVARIANTS
ARISING FROM Uq(osp(1|2n)) AND U−q(so(2n + 1))

SACHA C. BLUMEN
School of Mathematics and Statistics,
The University of Sydney, NSW, 2006, Australia.

ABSTRACT

The Uq(osp(1|2n)) and U−q(so(2n + 1)) quantum link invariants obtained by colouring each component of a link with the (2n + 1)-dimensional irreducible representations of each quantum algebra, respectively, are the same up to a possibly obscure substitution of variables.

These quantum link invariants are identical to the Kauffman link invariants obtained from two isomorphic specialisations of the Birman-Wenzl-Murakami algebra. Each of these Kauffman link invariants is the trace of some element in the relevant specialisation of the Birman-Wenzl-Murakami algebra.

The truncated Bratteli diagrams of the semisimple quotients of these two specialisations of the Birman-Wenzl-Murakami algebra are the same, where the quotients are taken with respect to an ideal generated by a subset of elements with zero trace.

The trace of any element in one specialisation of the Birman-Wenzl-Murakami algebra is the same as the trace of the corresponding element in the other specialisation of the Birman-Wenzl-Murakami algebra up to a possibly obscure substitution of variables. This gives the corresponding result for the relevant uncoloured quantum link invariants.

Keywords: link invariants, quantum algebra, Birman-Wenzl-Murakami algebra

Mathematics Subject Classification 2000: 57M27, 17B37

3 Responses to Paper submitted to J. Knot Theory and Its Ramifications

  1. Darlene says:

    I was reading the Journal of Knot Theory and its Ramifications on the tram last night.

    Not sure where the article about Anna Nicole was.

    Having that sort of knowledge is very impressive (the maths stuff, not about Anna Nicole).

    I hope they publish your paper.

  2. Sacha says:

    Thanks Darlene!

  3. […] decomposing corpse of Anna Nicole Smith in ‘Knot’, the very intelligent Sacha Blumen may have an article published in it […]

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