The University of Queensland

Centre for Mathematical Physics

SEMINAR

Speaker: Dr Jorgen Rasmussen,

Department of Mathematics and Statistics,

The University of Melbourne

Title: Fusion algebra of logarithmic minimal models

2pm, Thursday 11^th October, 2007

Priestley Building, room 641

Abstract:

The logarithmic minimal models were introduced recently as the conformal scaling limits of certain lattice models described in terms of the planar Temperley-Lieb algebra. Fusion of the associated Virasoro representations can be implemented on the lattice and we discuss the ensuing fusion algebras. They are both commutative and associative but involve infinitely many generators. Among these are the so-called Kac representations which are typically reducible yet indecomposable Virasoro representations of rank 1. In particular, the identity of the fundamental fusion algebra is in general a reducible yet indecomposable Kac representation of rank 1. Indecomposable representations of rank 2 or 3 also appear and all the participating representations can be associated to an infinitely extended Kac table. Much of this is contrary to the well-known rational minimal models whose fusion algebras are generated by a finite number of representations all of which are irreducible.

All interested are invited to attend.

Enquiries to Katrina Hibberd email: keh@maths.uq.edu.au