The affine Demazure modules are the Demazure modules that occur in a level $\ell$ irreducible integrable representation of an affine Lie algebra. We call them $\mathfrak{g}$-stable if they are stable under the action of the standard maximal parabolic subalgebra of the affine Lie algebra. We prove that such a $\mathfrak{g}$-stable affine Demazure module is isomorphic to the fusion (tensor) product of smaller $\mathfrak{g}$-stable affine Demazure modules, 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 the decomposition of $\mathfrak{g}$-stable affine Demazure modules. Our proof for this key fact is uniform, avoids the case-by-case analysis, and works for all finite-dimensional simple Lie algebras.

- All seminars.
- Seminars for 2020

Last updated: 18 Apr 2021