Characteristic polynomials and finitely dimensional representations of $\mathfrak{sl}(2, \mathbb{C})$

Abstract

In this paper, we obtain a general formula for the characteristic polynomial of a finitely dimensional representation of Lie algebra sl(2, C) and the form for these characteristic polynomials, and prove there is one to one correspondence between representations and their characteristic polynomials. We define a product on these characteristic polynomials, endowing them with a monoid structure.