A note on the fusion product decomposition of Demazure modules

Abstract

We settle the fusion product decomposition theorem for higher level affine Demazure modules for the cases E (1) 6,7,8 , F (1) 4 and E (2) 6 , thus completing the main theorems of Chari et al. (J. Algebra, 2016) and Kus et al. (Represent. Theory, 2016). 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.