A Note on the Fusion Product Decomposition of Demazure Modules

We settle the fusion product decomposition theorem for higher level affine Demazure modules for the cases E-6,7,8((1)), F-4((1)) and E-6((2)), thus completing the main theorems of V. Chari et al. [J. Algebra 455 (2016) 314-346] and D. Kus et al. [Representation Theory 20 (2016) 94-127]. We obtain a new combinatorial proof for the key fact, that was used in Chari et al. (op. cit.), to prove this decomposition theorem. We give a case free uniform proof for this key fact.