W-extended fusion algebra of critical percolation

Abstract

Two-dimensional critical percolation is the member of the infinite series of Yang-Baxter integrable logarithmic minimal models . We consider the continuum scaling limit of this lattice model as a 'rational' logarithmic conformal field theory with extended symmetry and use a lattice approach on a strip to study the fundamental fusion rules in this extended picture. We find that the representation content of the ensuing closed fusion algebra contains 26 -indecomposable representations with eight rank-1 representations, 14 rank-2 representations and four rank-3 representations. We identify these representations with suitable limits of Yang-Baxter integrable boundary conditions on the lattice an..