Related papers: Superintegrability summary
The wonderful formulas by I.Dumitriu and A.Edelman rewrite $\beta$-ensemble, with eigenvalue integrals containing Vandermonde factors in the power $2\beta$, through integrals over tridiagonal matrices, where $\beta$-dependent are the powers…
Fermionic-type character formulae are presented for charged irreduciblemodules of the graded parafermionic conformal field theory associated to the coset $osp(1,2)_k/u(1)$. This is obtained by counting the weakly ordered `partitions'…
The supersymmetric Poisson Sigma model is studied as a possible worldsheet realization of generalized complex geometry. Generalized complex structures alone do not guarantee non-manifest N=(2,1) or N=(2,2) supersymmetry, but a certain…
New types of irreducible second order Darboux transformations for the one dimensional Schroedinger equation are described. The main feature of such transformations is that the transformation functions have the eigenvalues grater then the…
We study a generalized scheme of Swanson Hamiltonian from a second-derivative pseudosupersymmetric approach. We discuss plausible choices of the underlying quasi-Hamiltonian and consider the viability of applications to systems like the…
We inquire into some properties of diagonalizable pseudo-Hermitian operators, showing that their definition can be relaxed and that the pseudo-Hermiticity property is strictly connected with the existence of an antilinear symmetry. This…
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general associative cubic algebra and we present specific…
For the simplest case of a supermembrane matrix model, various symmetry reductions are given, with the fermionic contribution(s) (to an effective Schr\"odinger equation) corresponding to an attractive $\delta$-function potential (towards…
This work is devoted to the investigation of the quantum mechanical systems on the two dimensional hyperboloid which admit separation of variables in at least two coordinate systems. Here we consider two potentials introduced in a paper of…
We reconsider light-cone superstring field theory on the maximally supersymmetric pp-wave background. We find that the results for the fermionic Neumann matrices given so far in the literature are incomplete and verify our expressions by…
We give a criterion for higher-dimensional Gaussian Gabor frames, which is a reformulation of one of the main results in in a previous article by the first and last authors in more explicit terms. We use this formulation in order to extend…
We give a combinatorial characterization of the identities holding in the semiring of all upper triangular Boolean $n\times n$-matrices and apply the characterization to computational complexity of identity checking, finite axiomatizability…
We introduce a canonical form for reduced bases of integral closures of discrete valuation rings, and we describe an algorithm for computing a basis in reduced normal form. This normal form has the same applications as the Hermite normal…
We give divisibility results for the (global) characteristic varieties of hypersurface complements expressed in terms of the local characteristic varieties at points along one of the irreducible components of the hypersurface. As an…
A notion of a particular integrability is introduced when two operators commute on a subspace of the space where they act. Particular integrals for one-dimensional (quasi)-exactly-solvable Schroedinger operators and Calogero-Sutherland…
A thorough account is given of the derivation of uniform semiclassical approximations to the particle and kinetic energy densities of N noninteracting bounded fermions in one dimension. The employed methodology allows the inclusion of…
The standard model ascribes distinct properties to different chiralities of fermions. We show how to incorporate this aspect in an extended spacetime-property framework involving two different attributes using a generalized metric which…
In this paper the notion of a superconformal structure on a supermanifold is introduced in an effort to study the superparticle sigma-model. There are, in particular, two main aspects of the sigma-model which are investigated. The first is…
The scalar fields of supersymmetric models are coordinates of a geometric space. We propose a formulation of supersymmetry that is covariant with respect to reparametrizations of this target space. Employing chiral multiplets as an example,…
In the present work we show that the joint probability distribution of the eigenvalues can be expressed in terms of a differential operator acting on the distribution of some other matrix quantities. Those quantities might be the diagonal…