A decomposition theorem for Demazure crystals.
Let \(\mathfrak g\) be a symmetrizable Kac-Moody Lie algebra. In [Ann. Sci. Éc. Norm. Supér. (4) 18, No. 3, 389--419 (1985; Zbl 0589.22014)], Section 5.8, the author raised the question whether the tensor product of an integrable module with a Demazure module admits a filtration whose quotients are Demazure modules. The interest lies in the fact that one could then use the Demazure expression to compute multiplicities. This has been studied by various researchers. In this paper, the author addresses the crystal version of this problem in a purely combinatorial fashion. A new result is a computationally effective manner of obtaining multiplicities. Combined with the Demazure character formula he obtains some combinatorial identities.
scientific article; zbMATH DE number 1963608
scientific article