Related papers: Once More about Spectral-Dependent Quantum $R$-Mat…
The present work splits in two parts: first, we perform a straightforward generalization of results from [Re], proving autoquasitriangularity of quantum groups $ U_q(\frak{g}) $ and their unrestricted specializations at roots of 1, in…
Using parafermionic field theoretical methods, the fundamentals of 2d fractional supersymmetry ${\bf Q}^{K} =P$ are set up. Known difficulties induced by methods based on the $U_{q}(sl(2))$ quantum group representations and non commutative…
This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The…
Reflection and braid equations for rank two $q$-tensors are derived from the covariance properties of quantum vectors by using the $R$-matrix formalism.
We develop a unified method to study spectral determinants for several different manifolds, including spheres and hemispheres, and projective spaces. This is a direct consequence of an approach based on deriving recursion relations for the…
We calculate commutation relations of vertex operators for the spin representation of $U_q(D_n^{(1)})$ by using recursive formulae of R-matrices. In quantum symmetry approach, we obtain the energy and momentum spectrum of the quantum spin…
Inspired from modern out-of-equilibrium statistical physics models, a matrix product based framework permits the formal definition of random vectors (and random time series) whose desired joint distributions are a priori prescribed. Its key…
We consider a hierarchy of many particle systems on the line with polynomial potentials separable in parabolic coordinates. Using the Lax representation, written in terms of $2\times 2$ matrices for the whole hierarchy, we construct the…
We give explicit formulas for the intertwinors on the differential form bundles over $S^{p-1} \times S^{q-1}$ with the standard pseudo-Riemannian metric $g=-g_{{}_{S^{p-1}}}+g_{{}_{S^{q-1}}}$ of signature $(p-1,q-1)$. As a special case, we…
We construct representations $\hat\pi_{\br}$ of the quantum algebra $U_q(sl(n))$ labelled by $n-1$ complex numbers $r_i$ and acting in the space of formal power series of $n(n-1)/2$ non-commuting variables. These variables generate a flag…
For powder samples of polynuclear metal complexes the dependence of the inelastic neutron scattering intensity on the momentum transfer Q is known to be described by a combination of so called interference terms. They reflect the interplay…
We consider the differential system $y'-x^{-1}Ay-q(x)y=\rho By $ with $n\times n$ matrices $A,B, q(x)$, where $A,B$ are constant, $B$ is diagonal, $A$ and $q(x)$ are off-diagonal, $q(\cdot)\in W^1_1[0,\infty)$. Some distinguished…
A rotor system, having the symmetry afforded by the two-parameter quantum algebra Uqp(u(2)), is investigated in this communication. This system is useful in rotational spectroscopy of molecules and nuclei. In particular, it is shown to lead…
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…
Results obtained by us are overviewed from a general set up. The universal $R$-matrix is exploited to obtain various important relations and structures involved in quantum group algebra, which are used subsequently for generating different…
We obtain the basic $R$-matrix of the two-parameter Quantum group $U=U_{r,s}\mathcal(\mathfrak{so}_{2n})$ via its weight representation theory and determine its $R$-matrix with spectral parameters for the two-parameter quantum affine…
We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…
We reinvestigate the momentum-resolved single-particle spectral function of the Tomonaga-Luttinger model. In particular, we focus on the role of the momentum-dependence of the two-particle interaction V(q). Usually, V(q) is assumed to be a…
A general unifying framework for integrable soliton-like systems on time scales is introduced. The $R$-matrix formalism is applied to the algebra of $\delta$-differential operators in terms of which one can construct infinite hierarchy of…
Two trace formulas for the spectra of arbitrary Hermitian matrices are derived by transforming the given Hermitian matrix $H$ to a unitary analogue. In the first type the unitary matrix is $e^{i(\lambda\II - H)}$ where $\lambda$ is the…