Tau-functions as highest weight vectors for W_{1+infty} algebra

Abstract

For 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 added

References in corpus (1)

• Highest weight modules of W_{1+infty}, Darboux transformations and the bispectral problem

Cited by in corpus (4)

• Bispectral algebras of commuting ordinary differential operators
• Highest weight modules of W_{1+infty}, Darboux transformations and the bispectral problem
• W_{N+1}-constraints for singularities of type A_N
• Bäcklund--Darboux transformations in Sato's Grassmannian