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arXiv · 2510.11510

The Gelfand-Tsetlin type base for the algebra $\mathfrak{g}_2$

Dmitry Artamonov
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Abstract

The paper presents a construction of finite-dimensional irreducible representations of the Lie algebra $\mathfrak{g}_2$. The representation space is constructed as the space of solutions to a certain system of partial differential equations of hypergeometric type, which is closely related to the Gelfand-Kapranov-Zelevinsky systems. This connection allows for the construction of a basis in the representation. The orthogonalization of the constructed basis with respect to the invariant scalar product turns out to be a Gelfand-Tsetlin-type basis for the chain of subalgebras $\mathfrak{g}_2 \supset \mathfrak{sl}_3$.

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BibTeXRIS

Dmitry Artamonov. 2025-10-13. The Gelfand-Tsetlin type base for the algebra $\mathfrak{g}_2$. https://arxiv.org/abs/2510.11510

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