Tudose Geanina - Littlewood-Richardson rule for a special case of fusion coefficients

The fusion coefficients are the structure constants associated to the fusion algebra of an affine Kac-Moody algebra , which can be seen as truncated tensor product coefficients at level k. For g=A_n-1 Goodman and Wenzl have an equivalent interpretation to the Hecke algebra at root of unity. Using this we are able to give a combinatorial interpretation of these coefficients for the case where one of the weights is a 2-column partition. In this talk we will describe this interpretation and some applications of it.