Kaul, R. K.
(1994)
*The representations of Temperley-Lieb-Jones algebras*
Nuclear Physics - Section B: Particle Physics, Field Theory and Statistical Systems, Physical Mathematics, 417
(1-2).
pp. 267-285.
ISSN 0550-3213

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/055032...

Related URL: http://dx.doi.org/10.1016/0550-3213(94)90547-9

## Abstract

Representations of the braid group obtained from rational conformal field theories can be used to obtain explicit representations of Temperley-Lieb-Jones algebras. The method is described in detail for SU(2)_{k} Wess-Zumino conformal field theories and its generalization to an arbitrary rational conformal field theory is outlined. Explicit definition of an associated linear trace operation in terms of a certain matrix element in the space of conformal blocks of such a conformal theory is presented. Further, for every primary field of a rational conformal field theory, there is a subfactor of the hyperfinite II_{1} factor with trivial relative commutant. The index of the subfactor is given in terms of the identity-identity element of a certain duality matrix for the conformal blocks of the four-point correlators. Jones' formula for the index (< 4) for subfactors corresponds to the spin-1/2 representation of the SU(2)_{k} Wess-Zumino conformal field theory. The definition of the trace operation also provides a method of obtaining link invariants explicitly.

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ID Code: | 16446 |

Deposited On: | 15 Nov 2010 13:39 |

Last Modified: | 06 Jun 2011 04:45 |

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