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

Tianyi Jiang; Shoumin Liu

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arXiv · 2112.07933

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

Tianyi Jiang·Shoumin Liu

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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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BibTeX RIS

Tianyi Jiang, Shoumin Liu. 2021-12-15. Characteristic polynomials and finitely dimensional representations of $\mathfrak{sl}(2, \mathbb{C})$. https://arxiv.org/abs/2112.07933

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