Corpus ID: 232240106

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

@inproceedings{Lu2021GelfandTsetlinBO,
  title={Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra},
  author={Kang-Ya Lu},
  year={2021}
}
  • K. Lu
  • Published 15 March 2021
  • Mathematics
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 Y(gl1|1)-modules and show that a finite-dimensional irreducible Y(gl1|1)-module is tame if and only if it is thin. We also give the analogous statements for quantum affine superalgebra of type A. 
A note on odd reflections of super Yangian and Bethe ansatz
  • Kang Lu
  • Mathematics, Physics
  • 2021
In a recent paper [Mol21a], Molev introduced analogues of the odd reflections for the super Yangian Y(glm|n) and obtained a transition rule for the change of highest weights when the parity sequenceExpand
Schur-Weyl duality for quantum toroidal superalgebras
  • Kang Lu
  • Mathematics
  • 2021
We establish the Schur-Weyl type duality between double affine Hecke algebras and quantum toroidal superalgebras, generalizing the well known result of Vasserot-Varagnolo [VV96] to the super case.

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