Gelfand-Tsetlin Modules for Lie Algebras of Rank 2

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

doi:10.29020/nybg.ejpam.v18i3.6458

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Gelfand-Tsetlin Modules for Lie Algebras of Rank 2

Milica Anđelić Carlos M. da Fonseca Vyacheslav Futorny Andrew Tsylke

Year: 2025 Journal: European Journal of Pure and Applied Mathematics Vol: 18 (3)Pages: 6458-6458

DOI: 10.29020/nybg.ejpam.v18i3.6458

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Abstract

We explicitly construct families of simple modules for all simple Lie algebras of rank $2$ on which a certain commutative subalgebra acts diagonally with a simple spectrum. In type $A$, these modules are the well-known generic Gelfand-Tsetlin modules.

Keywords:

Mathematics Rank (graph theory) Lie algebra Algebra over a field Pure mathematics Combinatorics

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Algebraic structures and combinatorial models

Physical Sciences → Mathematics → Geometry and Topology

Advanced Algebra and Geometry

Physical Sciences → Mathematics → Mathematical Physics

Advanced Topics in Algebra

Physical Sciences → Mathematics → Algebra and Number Theory

Gelfand-Tsetlin Modules for Lie Algebras of Rank 2

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