Exotic Bialgebra S03: Representations, Baxterisation and Applications

Details Exotic Bialgebra S03: Representations, Baxterisation and Applications Exotic Bialgebra S03: Representations, Baxterisation and Applications

2006-01-29

arxiv.org/abs/math/0601708v2

Annales Henri Poincare, 7 (2006) 1351-73

Mathematics

Quantum Algebra

24 pages, Latex; V2: revised subsection 4.1, added 9 references, to appear in Annales Henri Poincare in the volume dedicated t

Scientific paper

10.1007/s00023-006-0283-7

The exotic bialgebra S03, defined by a solution of the Yang-Baxter equation, which is not a deformation of the trivial, is considered. Its FRT dual algebra $s03_F$ is studied. The Baxterisation of the dual algebra is given in two different parametrisations. The finite-dimensional representations of $s03_F$ are considered. Diagonalisations of the braid matrices are used to yield remarkable insights concerning representations of the L-algebra and to formulate the fusion of finite-dimensional representations. Possible applications are considered, in particular, an exotic eight-vertex model and an integrable spin-chain model.

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