Quantum R matrix for G2and a solvable 175-vertex model

DOI10.1088/0305-4470/23/8/011zbMath0715.17018OpenAlexW2077575034MaRDI QIDQ3202273

Atsuo Kuniba

Publication date: 1990

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0305-4470/23/8/011

zbMATH Keywords

representationYang-Baxter equationquantum groupsaffine Lie algebrassolvable modelCartan's exceptional simple Lie algebra

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Exactly solvable models; Bethe ansatz (82B23)

Related Items (12)

Quantum affine symmetry and scattering amplitudes of the imaginary coupled \(d_4^{(3)}\) affine Toda field theory ⋮ Vector version of Matsuo-Cherednik equation for the root system \(G_ 2\) ⋮ Solutions of the reflection equation for the \(U_q[G_2\) vertex model] ⋮ Quantum exceptional group \(G_2\) and its semisimple conjugacy classes ⋮ The spectrum properties of an integrable \(G_2\) invariant vertex model ⋮ Fusion \(U_q(G^{(1)}_2)\) vertex models and analytic Bethe ansätze ⋮ Diagonal \(K\)-matrices and transfer matrix eigenspectra associated with the \(G^{(1)}_2\) \(R\)-matrix ⋮ The trigonometric \(E_8\) \(R\)-matrix ⋮ Split Casimir operator for simple Lie algebras, solutions of Yang–Baxter equations, and Vogel parameters ⋮ Quantum R matrices related to the spin representations of \(B_ n\) and \(D_ n\) ⋮ Perfect crystals of \(U_q(G_2^{(1)})\) ⋮ On universal \(R\)-matrix for quantized nontwisted rank 3 affine KM algebras

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