English

Oscillator versus prefundamental representations II. Arbitrary higher ranks

Mathematical Physics 2017-09-27 v2 math.MP Exactly Solvable and Integrable Systems

Abstract

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

Keywords

Cite

@article{arxiv.1701.02627,
  title  = {Oscillator versus prefundamental representations II. Arbitrary higher ranks},
  author = {H. Boos and F. Göhmann and A. Klümper and Kh. S. Nirov and A. V. Razumov},
  journal= {arXiv preprint arXiv:1701.02627},
  year   = {2017}
}

Comments

26 pages, LaTeX2e; typos corrected, references with comments added. arXiv admin note: text overlap with arXiv:1512.04446, arXiv:1702.08710

R2 v1 2026-06-22T17:46:11.050Z