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

Shoumin Liu; Tianyi Jiang

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

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arxiv 2112.07933 v1 pith:GNB56RRI submitted 2021-12-15 math.RT

Tianyi Jiang , Shoumin Liu This is my paper · ORCID

classification math.RT

keywords characteristicpolynomialsdimensionalfinitelymathfrakrepresentationsalgebracorrespondence

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abstract

In this paper, we obtain a general formula for the characteristic polynomial of a finitely dimensional representation of Lie algebra $\mathfrak{sl}(2, \C )$ 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.

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