Gelfand-Tsetlin modules for Lie algebras of rank $2$

Milica Anđelić; Carlos M. da Fonseca; Vyacheslav Futorny; Andrew Tsylke

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arXiv · 2402.00483

Gelfand-Tsetlin modules for Lie algebras of rank $2$

Milica Anđelić·Carlos M. da Fonseca·Vyacheslav Futorny·Andrew Tsylke

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Abstract

We explicitly construct families of simple modules for Lie algebras of rank $2$, on which certain commutative subalgebra acts diagonally and has a simple spectrum. In type $A$ these modules are well known generic Gelfand-Tsetlin modules and they can be viewed as such for other rank $2$ Lie algebras.

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BibTeX RIS

Milica Anđelić, Carlos M. da Fonseca, Vyacheslav Futorny, Andrew Tsylke. 2024-02-01. Gelfand-Tsetlin modules for Lie algebras of rank $2$. https://arxiv.org/abs/2402.00483

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