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arXiv · 1907.07868

A note on $q$-oscillator realizations of $U_{q}(gl(M|N))$ for Baxter $Q$-operators

Zengo Tsuboi
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Abstract

We consider asymptotic limits of q-oscillator (or Heisenberg) realizations of Verma modules over the quantum superalgebra $U_{q}(gl(M|N))$, and obtain q-oscillator realizations of the contracted algebras proposed in [arXiv:1205.1471]. 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 $U_{q}(\hat{gl}(M|N))$ for Baxter Q-operators.

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Zengo Tsuboi. 2019-09-06. A note on $q$-oscillator realizations of $U_{q}(gl(M|N))$ for Baxter $Q$-operators. https://doi.org/10.1016/j.nuclphysb.2019.114747

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