QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains

Ferrando, Gwenaël; Frassek, Rouven; Kazakov, Vladimir

doi:10.48550/arxiv.2008.04336

Cited by 3 publications

(4 citation statements)

References 78 publications

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“…S(x) = 1 in the normalization of the R-matrices in[67]. But this is not the case with our R-matrices 21. The word 'irreducible' is not explicitly written in the corresponding proposition in[46].…”

mentioning

confidence: 86%

“…Baxter Q-operators for concrete physical models can be obtained by specifying representations of the Borel subalgebra. Much work has been done related to this 'q-oscillator construction' of Baxter Q-operators (see, for example, the following papers and references therein: [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] for the trigonometric case; [18,19,20,21] for the rational case; [22,23,24,25,26] for some other methods). Moreover, systematic studies related to this from the point of view of the asymptotic representation theory of quantum affine algebras were done in [27,28,29].…”

Section: Introductionmentioning

confidence: 99%

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Universal Baxter TQ-relations for open boundary quantum integrable systems

Tsuboi

2020

Preprint

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confidence: 86%

Section: Introductionmentioning

confidence: 99%

Universal Baxter TQ-relations for open boundary quantum integrable systems

Tsuboi

2020

Preprint

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“…These parallel lines are aligned along a direction of R 2 and are simultaneously crossed by a perpendicular magnetic 't Hooft line at z ′ = z. The 't Hooft line defect plays an important role in this modeling as it was interpreted in terms of the transfer (monodromy) matrix [3,5,25] and the Q-operators of the spin chain [13,26,27].…”

Section: Introductionmentioning

confidence: 99%

Lax operator and superspin chains from 4D CS gauge theory

Youssra¹,

Saidi²,

Laamara³

et al. 2022

J. Phys. A: Math. Theor.

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We study the properties of interacting line defects in the four-dimensional Chern Simons gauge theory with invariance given by the SL (m|n) super-group family. From this theory, we derive the oscillator realisation of the Lax operator for superspin chains with SL(m|n) symmetry. To this end, we investigate the holomorphic property of the bosonic Lax operator and build a diﬀerential equation describing the RLL eqs veriﬁed by this operator in the framework of the 4D CS gauge theory. We generalize this construction to the case of gauge super-groups, and develop a super-Dynkin diagram algorithm to deal with the decomposition of the Lie superalgebras. We obtain the generalisation of the Lax operator describing the interaction between the electric Wilson super-lines and the magnetic 't Hooft super-defects. This coupling is given in terms of a mixture of bosonic and fermionic oscillator degrees of freedom in the phase space of magnetically charged 't Hooft super-lines. The purely fermionic realisation of the superspin chain Lax operator is also investigated and it is found to coincide exactly with the ℤ2- gradation of Lie superalgebras.

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“…Connection to Grassmannians was elaborated on in [32]. Moreover, Wronskian-like solutions (scalar product of 'Q-vectors') of the T-system for U q (g (1) ) or Y (g) with g = D r , E n (n = 6, 7, 8) were proposed recently in [33], and in particular for g = D r case, a Wronskian-type expression from pure spinors, which uses a set of basic Q-functions different from the one used in the solution in [19], was presented (see also [34,35]). In this paper, we focus on the previously proposed Wronskian determinant solution for U q (B (1) r ) case [1], in relation to the CBR-type solution known in [2].…”

Section: Introductionmentioning

confidence: 99%

Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system

Tsuboi

2021

Preprint

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It is known that there is a correspondence between representations of superalgebras and ordinary (non-graded) algebras. Keeping in mind this type of correspondence between the twisted quantum affine superalgebra U q (gl(2r|1) (2) ) and the non-twisted quantum affine algebra U q (so(2r + 1) (1) ), we proposed, in the previous paper [1], a Wronskian solution of the T-system for U q (so(2r + 1) (1) ) as a reduction (folding) of the Wronskian solution for the non-twisted quantum affine superalgebra U q (gl(2r|1) (1) ). In this paper, we elaborate on this solution, and give a proof missing in [1]. In particular, we explain its connection to the Cherednik-Bazhanov-Reshetikhin (quantum Jacobi-Trudi) type determinant solution known in [2]. We also propose Wronskian-type expressions of T-functions (eigenvalues of transfer matrices) labeled by non-rectangular Young diagrams, which are quantum affine algebra analogues of the Weyl character formula for so(2r + 1). We show that T-functions for spinorial representations of U q (so(2r+1) (1) ) are related to reductions of T-functions for asymptotic typical representations of U q (gl(2r|1) (1) ).

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QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains

Cited by 3 publications

References 78 publications

Universal Baxter TQ-relations for open boundary quantum integrable systems

Universal Baxter TQ-relations for open boundary quantum integrable systems

Lax operator and superspin chains from 4D CS gauge theory

Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system

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