Verma Bases and Kashiwara-Nakashima Tableaux of ${\mathfrak{sp}}_4$

Abstract

We construct a one-to-one correspondence between the Verma basis vectors of a finite dimensional irreducible representation $L(\lambda )$ of the symplectic Lie algebra ${\mathfrak{sp}}_4$ and the Kashiwara-Nakashima tableaux of ${\mathfrak{sp}}_4$ with shape $\lambda$ naturally. We also give a proof of the linear independence of the Verma vector system directly.

17 pages