W-extended fusion algebras of logarithmic minimal models
by Jorgen Rasmussen
Abstract: We consider the continuum scaling limit of the infinite series of Yang-Baxter integrable logarithmic minimal models LM(p,p') as `rational'
logarithmic conformal field theories with extended W symmetry.
Critical dense polymers and critical percolation correspond to LM(1,2) and LM(2,3), respectively, and are used as illustrations. The W symmetry allows the countably infinite number of indecomposable Virasoro representations to be reorganized into a finite number of W-indecomposable representations. We classify these representations, which can have rank 1, 2 or 3, and discuss their characters. Using a lattice implementation of fusion on a strip, we determine the fusion rules for the W-indecomposable representations and find that they generate a closed fusion algebra, albeit one without identity for p 1.
For More Information: Contact: Iwan Jensen I.Jensen@ms.unimelb.edu.au