$\ell$-weights and factorization of transfer operators

Razumov, A. V.

doi:10.48550/arxiv.2103.16200

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“…Factorization of transfer operators. In this section we generalize the consideration given in the paper [28] for l = 1 and l = 2 to the case of general l. Below we treat the U q (L(sl l+1 ))-modules V µ ζ and V µ ζ as U q (L(b + ))-modules. Let us consider the following tensor product of l + 1 oscillator U q (L(b + ))-modules…”

Section: Case Of Oscillator Representationsmentioning

confidence: 94%

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Quantum groups and functional relations for arbitrary rank

Razumov

2021

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The quantum integrable systems associated with the quantum loop algebras U q (L(sl l+1 )) are considered. The factorized form of the transfer operators related to the infinite dimensional evaluation representations is found and the determinant form of the transfer operators related to the finite dimensional evaluation representations is obtained. The master TQ-and TT-relations are derived. The operatorial T-and Q-systems are found. The nested Bethe equations are obtained. CONTENTS A. V. RAZUMOV 5.3. Monodromy operators and transfer operators 27 5.4. L-operators and Q-operators 27 5.4.1. Definition 27 5.4.2. Case of oscillator representations 28 6. Functional relations 31 6.1. Factorization of transfer operators 31 6.2. Determinant representation 33 6.3. TQ-relations 35 6.4. TT-relations and T-system 36 6.5. Q-system and nested Bethe ansatz equations 37 7. Conclusion 40 Acknowledgments 41 Appendix A. Highest ℓ-weight of evaluation U q (L(sl l+1 ))-modules 41 References 43

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Section: Case Of Oscillator Representationsmentioning

confidence: 94%

“…In this paper, we use a different approach based on the analysis of the ℓ-weights of the representations. The effectiveness of the method was demonstrated in the paper [28] for l = 1 and l = 2. The present paper is devoted to the case of general l.…”

Section: Introductionmentioning

confidence: 99%