Related papers: Generic matrix superpotentials
Schroedinger equations with position dependent mass which are scale invariant and admit second order integrals of motion are classified.
The algebra of supernatural matrices is a key example in the theory of locally finite central simple algebras, which studied in a previous paper of the authors (\cite{Local}). It is also a stand-alone object admits a rich study and various…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible…
In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the…
We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the…
Self-similar potentials generalize the concept of shape-invariance which was originally introduced to explore exactly-solvable potentials in quantum mechanics. In this article it is shown that previously introduced algebraic approach to the…
We propose a new, exactly solvable Schr\"{o}dinger equation. The potential partner is given by \[{ V=}-Bp\operatorname{csch}[px]^{2}-9p(B+p)\operatorname*{sech}[3px]^{2}+(B\coth[px]-3(B+p)\tanh[3px])^{2}.\] obtained using supersymmetric…
The "2-variable general-$\lambda$-matrix polynomials (2VG$\lambda$MP)" is a new family of matrix polynomials, introduced and studied in this article. These matrix polynomials are constructed using umbral and symbolic methods. We delve into…
A simple construction of Whitham type hierarchies in all genera is suggested. Potentials of these hierarchies are written as integrals of hypergeometric type. Possible generalization for universal moduli space is also briefly discussed.
We consider nonnegative r-potent matrices with finite dimensions and study their decomposability. We derive the precise conditions under which an r-potent matrix is decomposable. We further determine a general structure for the r-potent…
As an extension of the intertwining operator idea, an algebraic method which provides a link between supersymmetric quantum mechanics and quantum (super)integrability is introduced. By realization of the method in two dimensions, two…
The fundamental matrix factorisations of the D-model superpotential are found and identified with the boundary states of the corresponding conformal field theory. The analysis is performed for both GSO-projections. We also comment on the…
We study four dimensional N=2 SO/SP supersymmetric gauge theory on R^3\times S^1 deformed by a tree level superpotential. We will show that the exact superpotential can be obtained by making use of the Lax matrix of the corresponding…
Some aspects of differential and integral calculi on generalized grassmann (paragrassmann) algebras are considered. The integration over paragrassmann variables is applied to evaluate the partition function for the $Z_{p+1}$ Potts model on…
The dimensions of sets of matrices of various types, with specified eigenvalue multiplicities, are determined. The dimensions of the sets of matrices with given Jordan form and with given singular value multiplicities are also found. Each…
The exact bound state spectrum of rationally extended shape invariant real as well as $PT$ symmetric complex potentials are obtained by using potential group approach. The generators of the potential groups are modified by introducing a new…
We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed…
We show how special forms of an $N=2$ Landau-Ginzburg potential directly imply the presence of an $N=2$ super-$W$ algebra. If the Landau-Ginzburg model has a super-$W$ algebra, we show how the elliptic genus can be refined so as to give…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…