Generalized Demazure modules and fusion products

Abstract

Let $\mathfrak{g}$ be a finite-dimensional complex simple Lie algebra with highest root $\theta$ and let $\mathfrak{g}[t]$ be the corresponding current algebra. In this paper, we consider the $\mathfrak{g}[t]$-stable Demazure modules associated to integrable highest weight representations of the affine Lie algebra $\hat{\mathfrak{g}}$. We prove that the fusion product of Demazure modules of a given level with a single Demazure module of a different level and with highest weight a multiple of $\theta$ is a generalized Demazure module, and also give defining relations. This also shows that the fusion product of such Demazure modules is independent of the chosen parameters. As a consequence we obtain generators and relations for certain types of generalized Demazure modules. We also establish a connection with the modules defined by Chari and Venkatesh.

24 pages; minor revisions

References in corpus (3)

• Fusion products and toroidal algebras
• Demazure Modules, Chari-Venkatesh Modules and Fusion Products
• A Steinberg type decomposition theorem for higher level Demazure modules

Cited by in corpus (3)

• Reduced arc schemes for Veronese embeddings and global Demazure modules
• A note on the fusion product decomposition of Demazure modules
• Graded limits of simple tensor product of Kirillov-Reshetikhin modules for $U_q({\widetilde{\mathfrak{sl}}}_{n+1})$