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arXiv · 1701.02627

Oscillator versus prefundamental representations II. Arbitrary higher ranks

H. Boos·F. Göhmann·A. Klümper·Kh. S. Nirov·A. V. Razumov
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Abstract

We find the $\ell$-weights and the $\ell$-weight vectors for the highest $\ell$-weight $q$-oscillator representations of the positive Borel subalgebra of the quantum loop algebra $U_q(\mathcal L(\mathfrak{sl}_{l+1}))$ for arbitrary values of $l$. Having this, we establish the explicit relationship between the $q$-oscillator and prefundamental representations. Our consideration allows us to conclude that the prefundamental representations can be obtained by tensoring $q$-oscillator representations.

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H. Boos, F. Göhmann, A. Klümper, Kh. S. Nirov, A. V. Razumov. 2017-09-25. Oscillator versus prefundamental representations II. Arbitrary higher ranks. https://doi.org/10.1063/1.5001336

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