SPECIAL MODULES FOR R(PSL(2, q))

Let R be a fusion ring and R-C := R circle times C-Z be the corresponding fusion algebra. We first show that the algebra R(C )has only one left (right, two-sided) cell and the corresponding left (right, two-sided) cell module. Then we prove that, up to isomorphism, R(C )admits a unique special module, which is 1-dimensional and given by the Frobenius-Perron homomorphism FPdim. Moreover, as an example, we explicitly determine the special module of the interpolated fusion algebra R(PSL(2, q)):= r(PSL(2, q))circle times C-Z up to isomorphism, where r(PSL(2, q)) is the interpolated fusion ring with even q > 2.