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arXiv · 2112.14595

Gelfand--Dickey hierarchy, generalized BGW tau-function, and $W$-constraints

Di Yang·Chunhui Zhou
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Abstract

Let $r\geq 2$ be an integer. The generalized BGW tau-function for the Gelfand--Dickey hierarchy of $(r-1)$ dependent variables (aka the $r$-reduced KP hierarchy) is defined as a particular tau-function that depends on $(r-1)$ constant parameters $d_1,\dots,d_{r-1}$. In this paper we show that this tau-function satisfies a family of linear equations, called the $W$-constraints of the second kind. The operators giving rise to the linear equations also depend on $(r-1)$ constant parameters. We show that there is a one-to-one correspondence between the two sets of parameters.

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Di Yang, Chunhui Zhou. 2021-12-29. Gelfand--Dickey hierarchy, generalized BGW tau-function, and $W$-constraints. https://arxiv.org/abs/2112.14595

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