We establish a connection between the modern theory of Yangians and the classical construction of the Gelfand-Zetlin bases for the Lie algebra gln. Our approach allows us to produce the q-analogues of the Gelfand-Zetlin formulae in a straightforward way.
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Maxim Nazarov, Vitaly Tarasov, Yangians and Gelfand-Zetlin Bases. Publ. Res. Inst. Math. Sci. 30 (1994), no. 3, pp. 459–478DOI 10.2977/PRIMS/1195165907