Vyacheslav Futorny, Dimitar Grantcharov, Luis Enrique Ramirez, “Irreducible Generic Gelfand–Tsetlin Modules of <nobr>$\mathfrak{gl}(n)$</nobr>”, SIGMA, 2015, Volume 11,018, 13 pp.

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Irreducible Generic Gelfand–Tsetlin Modules of $\mathfrak{gl}(n)$

Vyacheslav Futorny^a, Dimitar Grantcharov^b, Luis Enrique Ramirez^a

^a Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo SP, Brasil
^b Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA

Abstract: We provide a classification and explicit bases of tableaux of all irreducible generic Gelfand–Tsetlin modules for the Lie algebra $\mathfrak{gl}(n)$.

Keywords: Gelfand–Tsetlin modules; Gelfand–Tsetlin basis; tableaux realization.

MSC: 17B67

Received: October 1, 2014; in final form February 24, 2015; Published online February 28, 2015

Language: English

DOI: 10.3842/SIGMA.2015.018