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 $E_{6,7,8}^{(1)},F_4^{(1)}$ and $E_6^{(2)}$, 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.

6 pages

References in corpus (1)

• Macdonald Polynomials and level two Demazure modules for affine ${\mathfrak{sl}}_{n+1}$