%A Harris, Pamela E
%A Lescinsky, Haley
%A Mabie, Grace
%D 2018
%T Lattice patterns for the support of Kostantâ€™s weight multiplicity formula on $\mathfrak{sl}_3(\mathbb{C})$
%K
%X The multiplicity of a weight in a finite-dimensional irreducible representation of the Lie algebra $\mathfrak{sl}_{3} (\mathbb{C}) $ can be computed via Kostant's weight multiplicity formula. This formula consists of an alternating sum over a finite group and involves a partition function. Our main result describes the terms that contribute nonzero values to this formula, as, in practice, most terms in the sum contribute a value of zero. By taking a geometric approach, we provide concrete visualizations of these sets for all pairs of integral weights $\lambda$ and $\mu$ of $\mathfrak{sl}_3(\mathbb{C})$ and show that the diagrams associated to our main result present new and surprising symmetry.
%U https://mjum.math.umn.edu/index.php/mjum/article/view/45
%J Minnesota Journal of Undergraduate Mathematics
%0 Journal Article
%V 4
%N 1
%@ 2378-5810
%8 2018-06-15