Related papers: Reflection operator and hypergeometry I: $SL(2, \m…
We present a necessary and sufficient condition for a finite-dimensional highest weight representation of the $sl_2$ loop algebra to be irreducible. In particular, for a highest weight representation with degenerate parameters of the…
Spectrum of a certain class of first order conformally invariant operators on the sphere is explicitly computed. The class contains the (elliptic verions of) Rarita-Schwinger operator and its higher spin analogues.
Let X=H\G be a homogeneous spherical variety for a split reductive group G over the integers o of a p-adic field k, and K=G(o) a hyperspecial maximal compact subgroup of G=G(k). We compute eigenfunctions ("spherical functions") on X=X(k)…
We solve the Klein-Gordon equation in the presence of the hyperbolic tangent potential. The scattering solutions are derived in terms of hypergeometric functions. The reflection $R$ and transmission $T$ coefficients are calculated in terms…
For the sl_2 Gaudin model (degenerated quantum integrable XXX spin chain) an exponential generating function of correlators is calculated explicitely. The calculation relies on the Gauss decomposition for the SL_2 loop group. From the…
This paper investigates the eigenvalue problem of integral operators whose kernels can be expressed as a finite sum of pairwise products of single-variable functions, making them separable. By consdiering the matrix form of the separable…
The reflection function of a smooth CR diffeomorphism between two minimal real analytic hypersurfaces is everywhere real analytic.
We quantise orbits of the adjoint group action on elements of the sl(2,R) Lie algebra. The path integration along elliptic slices is akin to the coadjoint orbit quantization of compact Lie groups, and the calculation of the characters of…
We introduce the notion of a family of convolution operators associated with a given elliptic partial differential operator. Such a convolution structure is shown to exist for a general class of Laplace-Beltrami operators on two-dimensional…
The Calogero model with external harmonic oscillator potential is discussed from sL(2,R) algebra point of view. Explicit formulae for functions with exponential time behaviour are given; in particular, the integrals of motion are…
Recent work on algebraic formulations of holographic dualities in terms of large $N$ algebras has revealed a deep connection between the properties of the associated spectral functions and the emergence of a semiclassical spacetime and…
Snell's law dictates the phenomenon of light refraction at the interface between two media. Here, we demonstrate arbitrary programming of light refraction through an engineered material where the direction of the output wave can be set…
A complete effective Hamiltonian for relativistic corrections at orders $m\alpha^6$ and $m\alpha^6(m/M)$ in a one-electron molecular system is derived from the NRQED Lagrangian. It includes spin-independent corrections to the energy levels…
We construct an operator system generated by $4$ operators that is not hyperrigid, although all restrictions of irreducible representations have the unique extension property.
Series of finite dimensional representations of the superalgebras spl(p,q) can be formulated in terms of linear differential operators acting on a suitable space of polynomials. We sketch the general ingredients necessary to construct these…
The matrix-valued spherical functions for the pair (K x K, K), K=SU(2), are studied. By restriction to the subgroup A the matrix-valued spherical functions are diagonal. For suitable set of representations we take these diagonals into a…
We show that several convolution operators on the space of entire functions, such as the MacLane operator, support a dense hypercyclic algebra that is not finitely generated. Birkhoff's operator also has this property on the space of…
Using as starting point a classical integral representation of a L-function we define a familly of two variables extended functions which are eigenfunctions of a Hermitian operator (having imaginary part of zeros as eigenvalues). This…
We study the elastic Herglotz wave functions, which are entire solutions of the spectral Navier equation appearing in the linearized elasticity theory with $L^2-$far-field patterns. We characterize in three-dimensions the set of these…
For the integrable spin-s XXZ chain we express explicitly any given spin-$s$ form factor in terms of a sum over the scalar products of the spin-1/2 operators. Here they are given by the operator-valued matrix elements of the monodromy…