By solving the infinitesimal Galilean symmetry for the KdV hierarchy, we obtain an explicit expression for the corresponding one-parameter Lie group, which we call the Galilean symmetry of the KdV hierarchy [1]. As an application, we establish an explicit relationship between the non-abelian Born–Infeld partition function and the generalized Brézin–Gross–Witten partition function. References: [1] Xu, J., Yang, D.: Galilean symmetry of the KdV hierarchy. J. Lond. Math. Soc.(2) 111 (2025), no. 2, Paper No. e70075.