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.

#### References

SHOWING 1-10 OF 49 REFERENCES
Gauss Decomposition of the Yangian Y (gl M|n )
Here we describe a Gauss decomposition of the Yangian Y (glm|n) of the general linear Lie superalgebra. This gives a connection between this Yangian and the Yangian of the classical Lie superalgebraExpand
On the Yangian Y(gl m|n ) and its quantum Berezinian
• Czech. J. Phys
• 2005
On the supersymmetric XXX spin chains associated to gl 1|1
• Commun. Math. Phys
• 2021
Gelfand-Tsetlin modules for gl(n,m)
• Mathematics
• 2020
We address the problem of classifying of irreducible Gelfand-Tsetlin modules for gl(m|n) and show that it reduces to the classification of Gelfand-Tsetlin modules for the even part. We also give anExpand
Jacobi–Trudi Identity and Drinfeld Functor for Super Yangian
• Mathematics, Physics
• 2020
We show that the quantum Berezinian which gives a generating function of the integrals of motions of XXX spin chains associated to super Yangian $\mathrm{Y}(\mathfrak{gl}_{m|n})$ can be written as aExpand
Poles of finite-dimensional representations of Yangians in type A
• Mathematics
• 2020
Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra over $\mathbb{C}$, and let $Y_{\hbar}(\mathfrak{g})$ be the Yangian of $\mathfrak{g}$. In this paper, we initiate the study of the set ofExpand
Yangian of the General Linear Lie Superalgebra
We prove several basic properties of the Yangian of the Lie superalgebra glM |N .
Solutions of glm|n XXX Bethe ansatz equation and rational difference operators
• J. Phys. A: Math. eor
• 2019
Length-Two Representations of Quantum Affine Superalgebras and Baxter Operators
Associated to quantum affine general linear Lie superalgebras are two families of short exact sequences of representations whose first and third terms are irreducible: the Baxter TQ relationsExpand
RTT realization of quantum affine superalgebras and tensor products
We use the RTT realization of the quantum affine superalgebra associated with the Lie superalgebra $\mathfrak{gl}(M,N)$ to study its finite-dimensional representations and their tensor products. InExpand