Combinatorial construction of Gelfand-Tsetlin modules for \mathfrakgl_n

2016/11/23 by Vyacheslav Futorny, Futorny, Vyacheslav, Luis Enrique Ramírez +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1611.07908

openalex publication_date 2016/11/23 · openalex created_date 2016/11/30 · openalex updated_date 2026/07/28

Abstract

We propose a new effective method of constructing explicitly Gelfand -Tsetlin modules for \mathfrakgl_n. We obtain a large family of simple modules that have a basis consisting of Gelfand-Tsetlin tableaux, the action of the Lie algebra is given by the Gelfand-Tsetlin formulas and with all Gelfand-Tsetlin multiplicities equal 1. As an application of our construction we prove necessary and sufficient condition for the Gelfand and Graev's continuation construction to define a module which was conjectured by Lemire and Patera.

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