Tau-functions as highest weight vectors for W1+infty algebra
Abstract
For each r = (r1, r2,...,rN) we construct a highest weight module Mr of the Lie algebra W1+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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