Irreducible Harish-Chandra modules over extended Witt algebras (Q2255156)

The extended Witt algebra of rank \(d\) is the semi-direct product of the rank \(d\) Witt algebra \(W\) with the Laurent polynomial ring \(A:=\mathbb{C}[t_1^{\pm 1},t_2^{\pm 1},\dots,t_d^{\pm 1}]\) on which \(W\) acts in the natural (defining) way. The paper under review provides a classification of simple weight modules with finite dimensional weight spaces on which \(A\) acts non-trivially, for this semi-direct product. The main result asserts that any such module is either the quotient of a generalized Verma module or is a deformation (more precisely, a twist by an automorphism of an algebra) of a uniformly bounded \(W\)-module from a family constructed in [\textit{S. Eswara Rao}, J. Math. Phys. 45, No. 8, 3322--3333 (2004; Zbl 1071.17020)].