PT symmetry and representations of the Temperley-Lieb algebra on the unit circle
Department of Mathematics, University of Glasgow
Mon, Nov. 26th 2007, 11:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
I will present ongoing work on representations of the
Temperley-Lieb algebra arising in connection with the $U_q(sl_2)$ invariant
XXZ spin-chain when the deformation parameter $q$ lies on the unit circle.
Using concepts from "non-Hermitian quantum mechanics" (namely PT-symmetry,
Bender's C-operator and quasi-Hermiticity) I will review the procedure
known as "quantum group reduction" and present some exact results
concerning the construction of an inner product which is invariant under
the action of the Temperley-Lieb algebra. For a particular section of the
unit circle I will present a novel formula for the invariant product which
can be evaluated using Kauffman diagrams.