2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/187173For each r = (r_1, r_2,...,r_N) we construct a highest weight module M_r of the Lie algebra W_{1+infty}. The highest weight vectors are specific tau-functions of the N-th Gelfand--Dickey hierarchy. We show that these modules are quasifinite and we give a complete description of the reducible ones together with a formula for the singular vectors. This paper is the first of a series of papers (q-alg/9602010, q-alg/9602011, q-alg/9602012) on the bispectral problem.13 pages, LaTeX2e, uses amsfonts.sty, no figures; references addedHigh Energy Physics - Theorytext