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An algebra-level version of a link-polynomial identity of Lickorish

Published online by Cambridge University Press:  01 May 2008

MICHAEL J. LARSEN  and
ERIC C. ROWELL
MICHAEL J. LARSEN
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A. e-mail: [email protected]
ERIC C. ROWELL
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843, U.S.A. e-mail: [email protected]
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Abstract

We establish isomorphisms between certain specializations of BMW algebras and the symmetric squares of Temperley–Lieb algebras. These isomorphisms imply a link-polynomial identity due to W. B. R. Lickorish. As an application, we compute the closed images of the irreducible braid group representations factoring over these specialized BMW algebras.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 144 , Issue 3 , May 2008 , pp. 623 - 638
Copyright
Copyright © Cambridge Philosophical Society 2008

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