arXiv subjects
Publications and source records attributed to Reinhard Häring-Oldenburg.
We introduce an Ariki-Koike like extension of the Birman-Murakami-Wenzl Algebra and show it to be semi-simple. This algebra supports a faithful Markov trace that gives rise to link invariants of closures of Coxeter type B braids.
A Potts model with a reflecting boundary is introduced and it is shown that its partition function can be expressed as a Markov trace on the Temperley-Lieb Algebra of Coxeter type B.
Braid groups may be defined for every Coxeter diagram. Artin's braid group is of type A. Analogs of Temperley-Lieb, Hecke and Birman-Wenzl algebras exist for B-type. Our general hypothethis is that the braid group of B-type replaces Artin's braid group in most physical applications if the model is equipped with a nontrivial boundary. Solutions of a Potts model with a boundary and the reflection equation illustrate this principle. Braided tensor categories of B-type and dually Coxeter-B braided Hopf algebras are introduced. The occurrence of such categories in QFT on a half plane is discussed.