Abstract

After reviewing briefly the basic notions of Lie algebras and Lie algebra representations, we delve into the construction of finite-dimensional representations of the general linear Lie algebra, 𝖌𝖑(𝑛). We will find some (in fact, all) of the finite-dimensional 𝖌𝖑(𝑛)-modules in the complex polynomial algebra, ℂ[𝑿], in the indeterminates in the 𝑛×𝑛 matrix and establish some combinatorics with Young tableaux.