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

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

1995-10-30

arxiv.org/abs/hep-th/9510211v3

J.Phys.A29:5565-5574,1996

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, LaTeX2e, uses amsfonts.sty, no figures; references added

Scientific paper

10.1088/0305-4470/29/17/027

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.

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