ABSTRACT
This chapter discusses the case of two colors, which seems to be the most important one from the subfactor point of view. It also discusses the certain generalizations of the Temperley-Lieb algebras depending on colors, which arise naturally as algebras of symmetries associated to intermediate subfactors. Repeating this procedure until either the spins don’t match or we have reached the two “outer” f’s, we obtain the following fusion rules. The chapter aims to structure of these higher relative commutants and computed their Bratelli diagram. The a’s on the top row, which are connected to the lines in the picture, are necessarily through strings, no matter how the letters on the boundary of the corresponding disk are connected.
