Free field approach to solutions of the quantum Knizhnik-Zamolodchikov equations.
Free field construction of D-branes in rational models of CFT and Gepner models.
From double Lie groups to quantum groups
It is shown, using geometric methods, that there is a C*-algebraic quantum group related to any double Lie group (also known as a matched pair of Lie groups or a bicrossproduct Lie group). An algebra underlying this quantum group is the algebra of a differential groupoid naturally associated with the double Lie group.
From noncommutative sphere to nonrelativistic spin.
Fundamental representations of Yangians and singularities of R-matrices.
Fusion algebras for superconformal field theories through coinvariants. II: super-Virasoro-symmetry.
Gaudin's model and the generating function of the Wroński map
We consider the Gaudin model associated to a point z ∈ ℂⁿ with pairwise distinct coordinates and to the subspace of singular vectors of a given weight in the tensor product of irreducible finite-dimensional sl₂-representations, [G]. The Bethe equations of this model provide the critical point system of a remarkable rational symmetric function. Any critical orbit determines a common eigenvector of the Gaudin hamiltonians called a Bethe vector. In [ReV], it was shown that for generic...
Gauge groups and topological invariants of vacuum manifolds
Gauge theories on deformed spaces.
Generalization of Okamoto's equation to arbitrary Schlesinger system.
Generalized coherent states for oscillators connected with Meixner and Meixner-Pollaczek polynomials.
Generalized coherent states for -oscillator associated with discrete -Hermite polynomials.
Generalized deformed commutation relations with nonzero minimal uncertainties in position and/or momentum and applications to quantum mechanics.
Generalized densities and distributional adjoints of natural operators.
Generalized Heisenberg algebras, SUSYQM and degeneracies: infinite well and Morse potential.
Generalized hermite polynomials obtained by embeddings of the q-Heisenberg algebra
Several ways to embed q-deformed versions of the Heisenberg algebra into the classical algebra itself are presented. By combination of those embeddings it becomes possible to transform between q-phase-space and q-oscillator realizations of the q-Heisenberg algebra. Using these embeddings the corresponding Schrödinger equation can be expressed by various difference equations. The solutions for two physically relevant cases are found and expressed as Stieltjes Wigert polynomials.
Generalized Hurwitz maps of the type S × V → W, anti-involutions, and quantum braided Clifford algebras
The notion of a -triple is studied in connection with a geometrical approach to the generalized Hurwitz problem for quadratic or bilinear forms. Some properties are obtained, generalizing those derived earlier by the present authors for the Hurwitz maps S × V → V. In particular, the dependence of each scalar product involved on the symmetry or antisymmetry is discussed as well as the configurations depending on various choices of the metric tensors of scalar products of the basis elements. Then...
Generalized radical rings, unknotted biquandles, and quantum groups
Generalized radical rings (braces) were introduced for the study of set-theoretical solutions of the quantum Yang-Baxter equation. We discuss their relationship to groups of I-type, virtual knot theory, and quantum groups.
Generating series and asymptotics of classical spin networks
We study classical spin networks with group SU. In the first part, using Gaussian integrals, we compute their generating series in the case where the edges are equipped with holonomies; this generalizes Westbury’s formula. In the second part, we use an integral formula for the square of the spin network and perform stationary phase approximation under some non-degeneracy hypothesis. This gives a precise asymptotic behavior when the labels are rescaled by a constant going to infinity.
Generating series for nested Bethe vectors.