Related papers: On the Clebsch-Gordan coefficients for the two-par…
The two-parametric quantum superalgebra $U_{p,q}[gl(2/2)]$ and its induced representations are considered. A method for constructing all finite-dimensional irreducible representations of this quantum superalgebra is also described in…
The two-parametric quantum deformation of the algebra of coordinate functions on the supergroup GL$(1| 1)$ via a contraction of GL$_{p,q}(1| 1)$ is presented. Related differential calculus on the quantum superplane is introduced.
We will derive both quaternion and octonion algebras as the Clebsch-Gordan algebras based upon the su(2) Lie algebra by considering angular momentum spaces of spin one and three. If we consider both spin 1 and 1/2 states, then the same…
We re-express the quantum Calogero-Sutherland model for the Lie algebra E7 and the particular value of the coupling constant K=1 by using the fundamental irreducible characters of the algebra as dynamical variables. For that, we need to…
The rotations, boosts, and translations in an N^2-dimensional spacetime are shown to be related to the fundamental commutators, anticommutators, and Clebsch-Gordan coefficients, respectively, of SU(N).
We develop a unified framework to compute band-geometric quantities in multiband systems whose low-energy Hamiltonians realize arbitrary $SU(2)$ representations. Exploiting the presence of a quantization axis, we use the Wigner--Eckart…
We establish a three-parameter Schur duality between the affine Hecke algebra of type C and a coideal subalgebra of quantum affine $\mathfrak{sl}_n$. At the equal parameter specializations, we obtain Schur dualities of types BCD.
We present a program that allows for the computation of tensor products of irreducible representations of Lie algebras A-G based on the explicit construction of weight states. This straightforward approach (which is slower and more…
Starting from the structural similarity between the quantum theory of gauge systems and that of the Kepler problem, an SU(2) gauge description of the five-dimensional Kepler problem is given. This non-abelian gauge system is used as a…
We use the theory of the quantum group $U_q(gl(2,\RR))$ in order to develop a quantum theory of invariants and show a decomposition of invariants into a Gordan-Capelli series. Higher binary forms are introduced on the basis of braided…
In a recent paper [J.-C. Pain, Opt. Spectrosc. ${\bf 218}$, 1105-1109 (2020)], we discussed the link between expectation values of powers of $r$ and Clebsch-Gordan coefficients. In this short note we provide additional information,…
In this paper, we characterize the multivariate uniform probability distribution of the first and second kinds in the framework of the $\mathcal{R}(p,q)$-deformed quantum algebras. Their bivariate distributions and related properties,…
We study quantum systems with even numbers N of levels that are completely state-controlled by unitary transformations generated by Lie algebras isomorphic to sp(N) of dimension N(N+1)/2. These Lie algebras are smaller than the respective…
In this paper, we show a condition for two-parameter Gorenstein cyclic quotient singularities to have a crepant resolution by using the remainder polynomial in any dimension.
We study relations between the two-parameter $\U_q(sl(n))$-invariant deformation quantization on $sl^*(n)$ and the reflection equation algebra. The latter is described by a quantum permutation on $\End(\C^n)$ given explicitly. The…
We consider GLq(N)-covariant quantum algebras with generators satisfying quadratic polynomial relations. We show that, up to some inessential arbitrariness, there are only two kinds of such quantum algebras, namely, the algebras with…
In this paper we show how all the quantum properties of Schroedinger and Pauli particles can be described entirely from within a Clifford algebra taken over the reals. There is no need to appeal to any `wave function'. To describe a quantum…
We study ${\cal N}=2$ SU(2) supersymmetric QCD with massive hypermultiplets deformed in the Nekrasov-Shatashvili limit of the Omega-background. The prepotential of the low-energy effective theory is determined by the WKB solution of the…
We find the Hopf algebra $U_{g,h}$ dual to the Jordanian matrix quantum group $GL_{g,h}(2)$. As an algebra it depends only on the sum of the two parameters and is split in two subalgebras: $U'_{g,h}$ (with three generators) and $U(Z)$ (with…
In a recent paper [1] we have constructed the spin and tensor representations of SO(4) from which the invariant weight can be derived for the Barrett-Crane model in quantum gravity. By analogy with the SO(4) group, we present the…