For the Lie algebra $\frak{sl}\_{n+1}$ we denote its fundamental irreducible representations by $V(\pi\_i)$, with $i=1, \dots, n$. Where can I find a table of the character formula (in other words a list of all the non-zero weight spaces of $V(\pi\_i)$ together with multiplicities)?


P.S. From this answer


[Fundamental representations and weight space dimension](https://mathoverflow.net/questions/314597/fundamental-representations-and-weight-space-dimension)


it looks that the multiplicities are also 1. So my question simplifies to a table of the non-zero weight spaces.



Character formula for the fundamental representations of $\frak{sl}_n$
These are examples of so called *minuscule* weights which are defined through the property that all the weights are given by $w\lambda$ where $\lambda$ is the highest weight and $w$ is an element of the Weyl group. So, in the $\mathfrak{sl}\_{n+1}$, to get all the weights in "the $\epsilon$ basis" you just take all possible permutations of coordinates of $\lambda$.


