Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 018, 13 pages      arXiv:1409.8413      https://doi.org/10.3842/SIGMA.2015.018
Contribution to the Special Issue on New Directions in Lie Theory

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

Vyacheslav Futorny a, Dimitar Grantcharov b and 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

Received October 01, 2014, in final form February 24, 2015; Published online February 28, 2015

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

Key words: Gelfand-Tsetlin modules; Gelfand-Tsetlin basis; tableaux realization.

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