Verma modules over generalized Virasoro algebras Vir[G]

Let F be a field of characteristic 0, not necessarily algebraically closed, and G be an additive subgroup of F. For any total order on G which is compatible with the group addition, and for any, (c) over dot is an element of F, a Verma module (M) over tilde((c) over dot, h) over the generalized Virasoro algebra Vir[G] is defined. In the present paper, the irreducibility of Verma modules (M) over tilde((c) over dot, h) is completely determined. (C) 2002 Elsevier Science B.V. All rights reserved.