GENERALIZED POLYNOMIAL MODULES OVER THE VIRASORO ALGEBRA

Let B-r be the (r + 1)-dimensional quotient Lie algebra of the positive part of the Virasoro algebra V. Irreducible B-r-modules were used to construct irreducible Whittaker modules in a work of Mazorchuk and Zhao (2014) and irreducible weight modules with infinite dimensional weight spaces over V in a work of Liu, Lu and Zhao (2015). In the present paper, we construct non-weight Virasoro modules F(M, Omega(lambda, beta)) from irreducible B-r-modules M and (A, V)-modules Omega(lambda, beta). We give necessary and sufficient conditions for the Virasoro module F(M, Omega(lambda, beta) to be irreducible. Using the weighting functor introduced by J. Nilsson, we also determine necessary and sufficient conditions for two F(M, Omega(lambda, beta) to be isomorphic.