Related papers: spl(p,q) superalgebra and differential operators

We examine applications of polynomial Lie algebras $sl_{pd}(2)$ to solve physical tasks in $G_{inv}$-invariant models of coupled subsystems in quantum physics. A general operator formalism is given to solve spectral problems using…

We study the representation theory of various convolution algebras attached to the $q$-deformation of $\mathrm{SL}(2,\mathbb{R})$ from an algebraic perspective and beyond the unitary case. We show that many aspects of the classical…

We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace both in the case where there are not central charges…

We exhibit a correspondence between subcategories of modules over an algebra and sub-bimodules of the dual of that algebra. We then prove that the semisimplicity of certain such categories is equivalent to the existence of a Peter-Weyl…

The quantum group SL_q(2,R) at roots of unity is introduced by means of duality pairings with the quantum algebra U_q(sl(2,R)). Its irreducible representations are constructed through the universal T-matrix. An invariant integral on this…

Consider the space B of complex $p\times q$ matrces with norm <1. There exists a standard one-parameter family $S_a$ of unitary representations of the pseudounitary group U(p,q) in the space of holomorphic functions on B (i.e. scalar…

The s ell_q(2) representations are realized in the space of polynomials for general and exceptional values of deformation parameter q and on finite set of theta-functions for cyclic representation corresponding to q^N = +/- 1, which are a…

Classification theorems for linear differential equations in two real variables, possessing eigenfunctions in the form of the polynomials (the generalized Bochner problem) are given. The main result is based on the consideration of the…

We introduce a notion of $(p,q)$-dominated multilinear operators which stems from the geometrical approach provided by $\Sigma$-operators. We prove that $(p,q)$-dominated multilinear operators can be characterized in terms of their behavior…

We investigate quantum deformation of conformal algebras by constructing the quantum space for $sl_q(4,C)$. The differential calculus on the quantum space and the action of the quantum generators are studied. We derive deformed $su(4)$ and…

It is shown that the deformed Heisenberg algebra involving the reflection operator R (R-deformed Heisenberg algebra) has finite-dimensional representations which are equivalent to representations of paragrassmann algebra with a special…

A notion of Drinfeld polynomials is introduced for modules of two-parameter quantum affine algebras. Finite dimensional representations are then characterized by sets of $l$-tuples of pairs of Drinfeld polynomials with certain conditions.

We consider the space of molecules endowed with the transpose version of the Chevet-Saphar norm and we identify its dual space with the space of Lipschitz strongly p-summing operators. We also extend some old results to the category of…

The main contribution of our paper is to give a partial classification of the quasi-exactly solvable Lie algebras of first order differential operators in three variables, and to show how this can be applied to the construction of new…

We compute the modular transformation formula of the characters for a certain family of (finitely or uncountably many) simple modules over the simple $\mathcal{N}=2$ vertex operator superalgebra of central charge…

A set of exactly solvable one-dimensional quantum mechanical potentials is described. It is defined by a finite-difference-differential equation generating in the limiting cases the Rosen-Morse, harmonic, and P\"oschl-Teller potentials.…

We introduce a noncommutative differential calculus on the two-parameter $h$-superplane via a contraction of the (p,q)-superplane. We manifestly show that the differential calculus is covariant under $GL_{h_1,h_2}(1| 1)$ transformations. We…

We introduce a category of $q$-oscillator representations over the quantum affine superalgebras of type $D$ and construct a new family of its irreducible representations. Motivated by the theory of super duality, we show that these…

Let $p<q$ be odd primes, $\rho_1$ and $\rho_2$ be irreducible representations of $\text{SL}(2,\mathbb{Z}_p)$ and $\text{SL}(2,\mathbb{Z}_q)$ of dimensions $\frac{p+1}{2}$ and $\frac{q+1}{2}$, respectively. We show that if…

We describe all of the irreducible polynomial $\mathbb{F}_p\mathrm{SL}_2(p^r)$ representations which lift to $(\mathbb{Z}/p^s\mathbb{Z})\mathrm{SL}_2(p^r)$ representations for $s>1$, observing that they almost never do. We also show that…