Integral representations and coherent states.
Internal Symmetries and Additional Quantum Numbers for Nanoparticles
Wavefunctions of symmetrical nanoparticles are considered making use of induced representation method. It is shown that when, at the same total symmetry, the order of local symmetry group decreases, additional quantum numbers are required for complete labelling of electron states. It is shown that the labels of irreducible representations of intermediate subgroups can be used for complete classification of states in the case of repeating IRs in symmetry adapted linear combinations. The intermediate...
Intertwining symmetry algebras of quantum superintegrable systems.
Introduction to noncommutative differential geometry.
Introduction to quantum Lie algebras
Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in h. They are derived from the quantized enveloping algebras . The quantum Lie bracket satisfies a generalization of antisymmetry. Representations of quantum Lie algebras are defined in terms of a generalized commutator. The recent general results about quantum Lie algebras are introduced with the help of the explicit example of .
Invariant symbolic calculus for compact Lie groups
We study the invariant symbolic calculi associated with the unitary irreducible representations of a compact Lie group.
Invariant symbolic calculus for semidirect products
Let be the semidirect product where is a connected semisimple non-compact Lie group acting linearly on a finite-dimensional real vector space . Let be a unitary irreducible representation of which is associated by the Kirillov-Kostant method of orbits with a coadjoint orbit of whose little group is a maximal compact subgroup of . We construct an invariant symbolic calculus for , under some technical hypothesis. We give some examples including the Poincaré group.
Invariants of three-manifolds, unitary representations of the mapping class group, and numerical calculations.
Jacobi operators of quantum counterparts of three-dimensional real Lie algebras over the harmonic oscillator
Operadic Lax representations for the harmonic oscillator are used to construct the quantum counterparts of three-dimensional real Lie algebras. The Jacobi operators of these quantum algebras are explicitly calculated.
Jordan-Schwinger representations and factorised Yang-Baxter operators.
Junction type representations of the Temperley-Lieb algebra and associated symmetries.
Kaehler coherent state orbits for representations of semisimple Lie groups
Kashaev's conjecture and the Chern-Simons invariants of knots and links.
Kernel functions for difference operators of Ruijsenaars type and their applications.
Killing spinor-valued forms and the cone construction
On a pseudo-Riemannian manifold we introduce a system of partial differential Killing type equations for spinor-valued differential forms, and study their basic properties. We discuss the relationship between solutions of Killing equations on and parallel fields on the metric cone over for spinor-valued forms.
Kreĭn spaces in de Sitter quantum theories.
Left-covariant differential calculi on
We study dimensional left-covariant differential calculi on the quantum group . In this way we obtain four classes of differential calculi which are algebraically much simpler as the bicovariant calculi. The algebra generated by the left-invariant vector fields has only quadratic-linear relations and posesses a Poincaré-Birkhoff-Witt basis. We use the concept of universal (higher order) differential calculus associated with a given left-covariant first order differential calculus. It turns out...
Limit distributions of many-particle spectra and q-deformed Gaussian variables
We find the limit distributions for a spectrum of a system of n particles governed by a k-body interaction. The hamiltonian of this system is modelled by a Gaussian random matrix. We show that the limit distribution is a q-deformed Gaussian distribution with the deformation parameter q depending on the fraction k/√n. The family of q-deformed Gaussian distributions include the Gaussian distribution and the semicircular law; therefore our result is a generalization of the results of Wigner [Wig1,...
Limits of Gaudin systems: classical and quantum cases.
Linear connections on almost commutative algebras.