A note on q-oscillator realizations of Uq(gl(M|N)) for Baxter Q-operators

Zengo Tsuboi

doi:10.1016/j.nuclphysb.2019.114747

Zengo Tsuboi

Open Access

https://doi.org/10.1016/j.nuclphysb.2019.114747

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Abstract

We consider asymptotic limits of q-oscillator (or Heisenberg) realizations of Verma modules over the quantum superalgebra Uq(gl(M|N)), and obtain q-oscillator realizations of the contracted algebras proposed in [1]. Instead of factoring out the invariant subspaces, we make reduction on generators of the q-oscillator algebra, which gives a shortcut to the problem. Based on this result, we obtain explicit q-oscillator representations of a Borel subalgebra of the quantum affine superalgebra Uq(glˆ(M|N)) for Baxter Q-operators.

Highlights

In the context of quantum integrable systems, the Baxter Q-operator [2] is a fundamental object
It is known that Baxter Q-operators can be constructed in terms of q-oscillator representations of one of the Borel subalgebras of quantum affine algebras
We have constructed q-oscillator realizations of the q-super-Yangian Yq(gl(M|N )) for Baxter Q-operators based on the Heisenberg realization of Uq(gl(M|N )) [24, 25]

Summary

Introduction

In the context of quantum integrable systems, the Baxter Q-operator [2] is a fundamental object. It is known that Baxter Q-operators can be constructed in terms of q-oscillator representations of one of the Borel subalgebras of quantum affine algebras. Hernandez and Jimbo showed [20] that the same type of q-oscillator representations can be systematically constructed by taking asymptotic limits of Kirillov-Reshetikhin modules over one of the Borel subalgebras of any non-twisted quantum affine algebra. This approach was further developed [21, 22] for Uq(sl(M|N)) case.

Quantum superalgebras

General strategy

Rational case

Concluding remarks