Introduction to Representation Theory
《Introduction to Representation Theory》 · 第 130 页 · Chapter 5，Section 5.23「Algebraic Representations of GL(V)」，Definition 5.23.1
Definition 5.23.1. We say that a finite dimensional representation $Y$ of $\mathrm{GL}(V)$ is algebraic (or rational, or polynomial) if its matrix elements are polynomial functions of the entries of $g, g^{-1}, g \in \mathrm{GL}(V)$ (i.e., belong to $k[g_{ij}][1/\det(g)]$).