ﻻ يوجد ملخص باللغة العربية
We collect and systematize general definitions and facts on the application of quantum groups to the construction of functional relations in the theory of integrable systems. As an example, we reconsider the case of the quantum group $U_q(mathcal L(mathfrak{sl}_2))$ related to the six-vertex model. We prove the full set of the functional relations in the form independent of the representation of the quantum group in the quantum space and specialize them to the case of the six-vertex model.
In this work we study an elliptic solid-on-solid model with domain-wall boundaries having the elliptic quantum group $mathcal{E}_{p, gamma}[widehat{mathfrak{gl}_2}]$ as its underlying symmetry algebra. We elaborate on results previously presented by
We consider a multichannel wire with a disordered region of length $L$ and a reflecting boundary. The reflection of a wave of frequency $omega$ is described by the scattering matrix $mathcal{S}(omega)$, encoding the probability amplitudes to be scatt
We study the joint probability density of the eigenvalues of a product of rectangular real, complex or quaternion random matrices in a unified way. The random matrices are distributed according to arbitrary probability densities, whose only restricti
We continue our exercises with the universal $R$-matrix based on the Khoroshkin and Tolstoy formula. Here we present our results for the case of the twisted affine Kac--Moody Lie algebra of type $A^{(2)}_2$. Our interest in this case is inspired by t
Standard derivations of the functional integral in non-equilibrium quantum field theory are based on the discrete time representation. In this work we derive the non-equilibrium functional integral for non-interacting bosons and fermions using a cont