Related papers: On osp(p+1,q+1|2r)-equivariant quantizations
We study two-parameter oscillator variations of the classical theorem on harmonic polynomials, associated with noncanonical oscillator representations of sl(n) and o(n). We find the condition when the homogeneous solution spaces of the…
We provide an explicit isomorphism between a quotient of the Bannai--Ito algebra and the Brauer algebra. We clarify also the connection with the action of the Lie superalgebra osp(1|2) on the threefold tensor product of its fundamental…
The quantum rotor is shown to be supersymmetric. The supercharge $Q$, whose square equals the Hamiltonian, is constructed with reflection operators. The conserved quantities that commute with $Q$ form the algebra $so(3)_{-1}$, an…
We define for real $q$ a unital $*$-algebra $U_q(\mathfrak{sl}(2,\mathbb{R}))$ quantizing the universal enveloping $*$-algebra of $\mathfrak{sl}(2,\mathbb{R})$. The $*$-algebra $U_q(\mathfrak{sl}(2,\mathbb{R}))$ is realized as a…
In [3], the authors showed the existence and the uniqueness of a sl(m+1,\R)-equivariant quantization in the non-critical situations. The curved generalization of the sl(m+1,\R)-equivariant quantization is the natural and projectively…
The paper contains essentially two new results. Physically, a deformation of the parastatistics in a sense of quantum groups is carried out. Mathematically, an alternative to the Chevalley description of the quantum orthosymplectic…
We prove two generalisations of the Binomial theorem that are also generalisations of the q-binomial theorem. These generalisations arise from the commutation relations satisfied by the components of the co-multiplications of non-simple…
A new "non-standard" quantization of the universal enveloping algebra of the split (natural) real form $so(2,2)$ of $D_2$ is presented. Some (classical) graded contractions of $so(2,2)$ associated to a $Z_2 \times Z_2$ grading are studied,…
We investigate a quantum system possessing a parasupersymmetry of order 2, an orthosupersymmetry of order $p$, a fractional supersymmetry of order $p+1$, and topological symmetries of type $(1,p)$ and $(1,1,...,1)$. We obtain the…
These notes describe some links between the group $\mathrm{SL}_2(\mathbb{R})$, the Heisenberg group and hypercomplex numbers---complex, dual and double numbers. Relations between quantum and classical mechanics are clarified in this…
We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or…
We prove existence results for optimization problems for the $k$th Laplace eigenvalue on closed Riemannian manifolds of dimension $m \geq 3$, depending on the choice of normalization. One such normalization leads to eigenvalue optimization…
There is a generalized oscillator-like algebra associated with every class of orthogonal polynomials $\{\Psi_n(x)\}_{n=0}^{\infty}$, on the real line, satisfying a four term non-symmetric recurrence relation…
In a recent paper characters and superdimension formulas were investigated for the class of representations with Dynkin labels $[0,\ldots,0,p]$ of the Lie superalgebra $osp(m|n)$. Such representations are infinite-dimensional, and of…
In earlier work of three of the authors of the present paper, a supercommutative quadratic algebra was associated to each symmetric quiver, and a new proof of positivity of motivic Donaldson-Thomas invariants of symmetric quivers was given…
In this paper, we consider the following overdetermined eigenvalue problem on an unbounded domain $\Omega\subset\mathbb{R}^{N+1}$ with $N\geq1$ \begin{equation} \left\{ \begin{array}{ll} -\Delta u=\lambda u\,\, &\text{in}\,\, \Omega,\\ u=0…
We show that the recently found covariant formulation for chiral $p$--forms in $2(p+1)$ dimensions with $p$ even, can be naturally extended to supersymmetric theories. We present the general method for writing covariant actions for chiral…
A nonpolynomial one-dimensional quantum potential representing an oscillator, that can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (harmonic oscillator with a centripetal barrier), is…
We study algebras satisfying a two-term multilinear identity, namely one of the form $x_1 \cdots x_n= q x_{\sigma(1)} \cdots x_{\sigma(n)}$, where $q$ is a parameter from the base field. We show that such algebras with $q=1$ and $\sigma$…
Classical and quantum superintegrable systems have a long history and they possess more integrals of motion than degrees of freedom. They have many attractive properties, wide applications in modern physics and connection to many domains in…