an:05190393
Zbl 1131.46042
Jones, Vaughan F. R.; Reznikoff, Sarah A.
Hilbert space representations of the annular Temperley-Lieb algebra
EN
Pac. J. Math. 228, No. 2, 219-249 (2006).
00211122
2006
j
46L37 16D60 57M27
planar algebras; subfactors; annular Temperley-Lieb; category; affine Hecke
Summary: The set of diagrams consisting of an annulus with a finite family of curves connecting some points on the boundary to each other defines a category in which a contractible closed curve counts for a certain complex number \(\delta\). For \(\delta = 2\cos(\pi/n)\), this category admits a \(C^*\)-structure and we determine all Hilbert space representations of this category for these values, at least in the case where the number of intemal boundary points is even. This result has applications to subfactors and planar algebras.