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arXiv · hep-th/9510211

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

B. Bakalov·E. Horozov·M. Yakimov
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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.

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B. Bakalov, E. Horozov, M. Yakimov. 1996-02-03. Tau-functions as highest weight vectors for W_{1+infty} algebra. https://doi.org/10.1088/0305-4470%2F29%2F17%2F027

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