  Let g be a semisimple Lie algebra over the complex numbers. Fix a positive
integer l (called the level). Let R(l,g) be the fusion algebra at level l.
Then, there is an algebra homomorphism from the representation ring R(g) of g
to R(l,g). We study a presentation of its kernel. The generators for the kernel
were given by Gepner, Gepner-Schwimmer, Bourdeau-Mlawer-Riggs-Schnitzer for g
of type A and C series. We make a conjecture for other classical groups and
also for g of type G2. We also have some partial results for F4 and E series.
