Weight modules over some Block algebras (Q1042915)

The author studies the Harish-Chandra modules and Verma modules over the Block algebra \(\mathfrak L[G]\). In case \(G\cong \mathbb Z^n\), the author obtains that the irreducible highest-weight module \(V(\phi)=M(\phi)/M'(\phi)\) is a Harish-Chandra module if there exists some exp-polynomial function \(\psi: \mathbb Z^n\rightarrow C\) and \(\phi\) is a mapping from \(L_0\) to \(\mathbb C\) induced by \(\psi\) in some way. The irreducible Harish-Chandra modules over \(\mathfrak L[G]\) has also been classified. Moreover, a criterion for irreducibility of the Verma module over the Block algebra \(\mathfrak L[G]\) is obtained.