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arxiv: 1701.02627 · v2 · pith:MBVMGNZKnew · submitted 2017-01-10 · 🧮 math-ph · math.MP· nlin.SI

Oscillator versus prefundamental representations II. Arbitrary higher ranks

classification 🧮 math-ph math.MPnlin.SI
keywords representationsoscillatorprefundamentalarbitraryweightalgebraallowsborel
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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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