Journal of the
Korean Mathematical Society JKMS

We give an explicit construction of Gr\"obner-Shirshov pairs and monomial bases for finite-dimensional irreducible representations of the simple Lie algebra $\mathfrak{sp}_4$. We also identify the monomial basis consisting of the reduced monomials with a set of semistandard tableaux of a given shape, on which we give a colored oriented graph structure.

Keywords: Grobner-Shirshov pair, monomial basis, representation, simple Lie algebra, Grobner-Shirshov graph

MSC numbers: 16Gxx