Classification of Simple Cuspidal Modules over a Lattice Lie Algebra of Witt type

Abstract

Let $W_{\pi }$ be the lattice Lie algebra of Witt type associated with an additive inclusion $\pi :{\mathbb{Z}}^N\hookrightarrow {\mathbb{C}}^2$ with $N>1$. In this article, the classification of simple ${\mathbb{Z}}^N$-graded $W_{\pi }$-modules, whose multiplicities are uniformly bounded, is given.

29 pages