Matrix model for the stationary sector of Gromov-Witten theory of ${\bf P}^1$

Abstract

In this paper we investigate the tau-functions for the stationary sector of Gromov-Witten theory of the complex projective line and its version, relative to one point. In particular, we construct the integral representation for the points of the Sato Grassmannians, Kac-Schwarz operators, and quantum spectral curves. This allows us to derive the matrix models.