Oscillator versus prefundamental representations. II. Arbitrary higher ranks

We find the ℓ -weights and the ℓ -weight vectors for the highest ℓ -weight q-oscillator representations of the positive Borel subalgebra of the quantum loop algebra U q ( L ( s l l + 1 ) ) for arbitrary values of l. Having this, we establish the explicit relationship between the q-oscillator and pre...

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Bibliographic Details
Published in:Journal of mathematical physics 2017-09, Vol.58 (9), p.1
Main Authors: Boos, Hermann, Göhmann, Frank, Klümper, Andreas, Nirov, Khazret S., Razumov, Alexander V.
Format: Article
Language:English
Subjects:
Algebra
Mathematical analysis
Oscillators
Physics
Quantum physics
Representations
Vectors (mathematics)
Weight
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Summary:We find the ℓ -weights and the ℓ -weight vectors for the highest ℓ -weight q-oscillator representations of the positive Borel subalgebra of the quantum loop algebra U q ( L ( s l 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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.5001336