Construction of eigenfunctions for a system of quantum minors of the monodromy matrix for an \(\mathrm{SL}(n,\mathbb{C})\)-invariant spin chain

DOI10.1134/S0040577916110015zbMath1362.82013MaRDI QIDQ520974

E. M. Uvarov, Pavel A. Valinevich, Petr P. Kulish, Sergey E. Derkachov

Publication date: 6 April 2017

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

intertwining operatorYang-Baxter equationseparation of variables\(R\)-matrixYangian

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Applications of Lie (super)algebras to physics, etc. (17B81) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Yang-Baxter equations (16T25)

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The Gelfand–Tsetlin basis for infinite-dimensional representations of gln(C), Separation of variables for rational \(\mathfrak{gl}(\mathsf{n})\) spin chains in any compact representation, via fusion, embedding morphism and Bäcklund flow, Unitarity of the SoV transform for \(\mathrm{SL}(2,\mathbb{C})\) spin chains, Separated variables and wave functions for rational gl(N) spin chains in the companion twist frame, Quantum integrability and quantum groups: a special issue in memory of Petr P Kulish, Separation of variables for the quantum \(\mathrm{SL} (3, \mathbb{C} )\) spin magnet: eigenfunctions of the Sklyanin \(B\)-operator, Construction of the Gelfand-Tsetlin basis for unitary principal series representations of the algebra \(sl_n(\mathbb{C})\)

Cites Work

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• Yang-Baxter equation and representation theory. I
• Drinfel'd twists and functional Bethe Ansatz
• Separation of variables in the quantum integrable models related to the Yangian \(\mathcal Y [sl (3)\)]
• Yangians and Gelfand-Zetlin bases
• Partition function of the eight-vertex lattice model
• Iterative construction of eigenfunctions of the monodromy matrix for $SL(2,\mathbb {C})$ magnet
• General solution of the Yang–Baxter equation with symmetry group $\mathrm {SL}(\mathit {n},\mathbb {C})$
• Integrability of scattering amplitudes inN= 4 SUSY
• Yangians and classical Lie algebras
• Representations of Yangians with GelfandZetlin bases
• THE CLASSICAL GROUPS. SPECTRAL ANALYSIS OF THEIR FINITE-DIMENSIONAL REPRESENTATIONS
• Noncompact Heisenberg spin magnets from high-energy QCD. I: Baxter Q-operator and separation of variables