Related papers: On $\tau^{(2)}$-model in Chiral Potts Model and Cy…
We obtain the Baxter Q-operators in the $U_q(\hat{sl}_2)$ invariant integrable models as a special limits of the quantum transfer matrices corresponding to different spins in the auxiliary space both from the functional relations and from…
In this paper, we present a systematical account of the descending procedure from six-vertex model to the $N$-state chiral Potts model through fusion relations of $\tau^{(j)}$-operators, following the works of Bazhanov-Stroganov and…
We study an integrable noncompact superspin chain model that emerged in recent studies of the dilatation operator in the N=1 super-Yang-Mills theory. It was found that the latter can be mapped into a homogeneous Heisenberg magnet with the…
Finite-dimensional representations of Onsager's algebra are characterized by the zeros of truncation polynomials. The Z_N-chiral Potts quantum chain hamiltonians (of which the Ising chain hamiltonian is the N=2 case) are the main known…
Integrable deformation of SU(2) sigma and lambda models are considered at the classical and quantum levels. These are the Yang-Baxter and XXZ-type anisotropic deformations. The XXZ type deformations are UV safe in one regime, while in…
It is shown that there is a hidden connection between the two well-studied sequences of the Temperley-Lieb (TL) integrable models -- the $q$-state quantum Potts (QP) models at the self-dual points and the staggered ${\rm SU}(n)$ spin-$s$…
We demonstrate that the $\tau^{(j)}$-matrices in the superintegrable chiral Potts model possess the Onsager algebra symmetry for their degenerate eigenvalues. The Fabricius-McCoy comparison of functional relations of the eight-vertex model…
We examine the Onsager algebra symmetry of $\tau^{(j)}$-matrices in the superintegrable chiral Potts model. The comparison of Onsager algebra symmetry of the chiral Potts model with the $sl_2$-loop algebra symmetry of six-vertex model at…
A very specific two-Higgs-doublet extension of the Glashow-Salam-Weinberg model for one generation of quarks is advocated for, in which the two doublets are parity transformed of each other and both isomorphic to the Higgs doublet of the…
The Baxter-Bazhanov-Stroganov model (also known as the \tau^(2) model) has attracted much interest because it provides a tool for solving the integrable chiral Z_N-Potts model. It can be formulated as a face spin model or via cyclic…
We consider the groundstate wave function and spectra of the $L$-site XXZ $U_q[s\ell(2)]$ invariant quantum spin chain with $q=\exp(\pi i/3)$. This chain is related to the critical Q=1 Potts model and exhibits $c=0$ conformal invariance. We…
Modular double of quantum group U_q (sl(2)) with deformation parameter q=e^{i\pi\tau} is a natural object explicitly taking into account the duality \tau -> 1/\tau. The use of the modular double in CFT allows to consider the region 1<c<25…
Starting with the Ising model, statistical models with global symmetries provide fruitful approaches to interesting physical systems, for example percolation or polymers. These include the $O(n)$ model (symmetry group $O(n)$) and the Potts…
We describe representation theory of the elliptic quantum group $E_{\tau,\eta}(sl_2)$. It turns out that the representation theory is parallel to the representation theory of the Yangian $Y(sl_2)$ and the quantum loop group $ U_q(\widetilde…
The transfer matrix of the XXZ open spin-1/2 chain with general integrable boundary conditions and generic anisotropy parameter (q is not a root of unity and |q|=1) is diagonalized using the representation theory of the q-Onsager algebra.…
Duality properties of the $SU(2)$ Principal Chiral Model are investigated starting from a one-parameter family of its equivalent Hamiltonian descriptions generated by a non-Abelian deformation of the cotangent space $T^*SU(2) \simeq SU(2)…
Bott and Samuelson constructed explicit cycles representing a basis of the Z_2-homology of the orbits of variationally complete representations of compact Lie groups. As a consequence, all those orbits are taut. We were able to show that an…
We consider irreducible cyclic representations of the algebra of monodromy matrices corresponding to the R-matrix of the six-vertex model. In roots of unity the Baxter Q-operator can be represented as a trace of a tensor product of…
Generalizing the mapping between the Potts model with nearest neighbor interaction and six vertex model, we build a family of "fused Potts models" related to the spin $k/2$ ${\rm U}_{q}{\rm su}(2)$ invariant vertex model and quantum spin…
The minimal Standard Model exhibits a nontrivial chiral U(2) symmetry if the vev and the hypercharge splitting (Delta) of right-handed leptons (quarks) in a family vanish and Q=T_0 + Y independently in each helicity sector. As a…