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

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 $\mathrm{Y}({\mathfrak{gl}}_{1|1})$-modules and show that a finite-dimensional irreducible $\mathrm{Y}({\mathfrak{gl}}_{1|1})$-module is tame if and only if it is thin. We also give the analogous statements for quantum affine superalgebra of type A.

arXiv comment23 pages. Final Version. To appear in Lett. Math. Phys

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Cited by in corpus (2)

• A note on odd reflections of super Yangian and Bethe ansatz
• Schur-Weyl duality for quantum toroidal superalgebras