School Seminars and Colloquia

Magical spectra and exceptional algebras

Mathematical Physics Seminar

by Jan de Gier


Institution: University of Melbourne
Date: Thu 28th April 2005
Time: 3:15 PM
Location: Room 213, Richard Berry Building, The University of Melbourne

Abstract: I will discuss the finite XXZ spin chain in the presence of non
spin-conserving boundaries. At some points in parameter space I will show
that it\'s spectrum has a large symmetry and that it suprisingly can be arranged,
for finite system sizes, according to N=1 or N=2 supersymmetry. It is further
shown that there is a precise spectral relation to a chain with spin-conservation
and quantum group symmetry. A \"proof\" of these numerically observed spectral
equivalences is given using the recently developed Bethe Ansatz equations for
the chain with open boundaries, and an expanation of this phenomenon lies in the
exceptional representation theory of the 1- and 2-boundary Temperley-Lieb algebra.

For More Information: Iwan Jensen tel. 8344-5214 e-mail: I.Jensen@ms.unimelb.edu.au