Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra

DOI10.1007/S11005-021-01488-WarXiv2103.08758MaRDI QIDQ6362943

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Publication date: 15 March 2021

Abstract: We give explicit actions of Drinfeld generators on Gelfand-Tsetlin bases of super Yangian modules associated with skew Young diagrams. In particular, we give another proof that these representations are irreducible. We study irreducible tame $mathrmY(mathfrak{gl}_{1|1})$-modules and show that a finite-dimensional irreducible $mathrmY(mathfrak{gl}_{1|1})$-module is tame if and only if it is thin. We also give the analogous statements for quantum affine superalgebra of type A.

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