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تسجيل مستخدم جديدOscillator versus prefundamental representations II. Arbitrary higher ranks
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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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For the case of quantum loop algebras $mathrm U_q(mathcal L(mathfrak{sl}_{l + 1}))$ with $l = 1, 2$ we find the $ell$-weights and the corresponding $ell$-weight vectors for the representations obtained via Jimbos homomorphism, known also as evaluatio
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