相关论文: Polynomial deformations of sl(2,R) in a three-dime…

We determine the group of linear transformations on a vector space $V$ that preserve a polynomial function $f$ on $V$ for several interesting pairs $(V,f)$, using the theory of semisimple algebraic groups.

The ${\mathcal D}$-pseudo-boson formalism is illustrated with two examples. The first one involves deformed complex Hermite polynomials built using finite-dimensional irreducible representations of the group ${\rm GL}(2,{\mathbb C})$ of…

Let K be a knot in $S^3$ and $X$ its complement. We study deformations of reducible metabelian representations of the knot group $\pi_1(X)$ into $SL(3,\mathbb{C})$ which are associated to a double root of the Alexander polynomial. We prove…

In the article, two implementations of the representation of the complex Lie algebra $\mathfrak{sl}_2$ on the algebra of symmetric polynomials $\Lambda_n$ by differential operators are proposed. The realizations of irreducible…

We introduce a new type of reduction of inversive difference polynomials that is associated with a partition of the basic set of automorphisms $\sigma$ and uses a generalization of the concept of effective order of a difference polynomial.…

We show that a new unitary transform with characteristics almost similar to those of the finite Fourier transform can be defined in any finite-dimensional Hilbert space. It is defined by using the Kravchuk polynomials, and we call it…

It is an open problem to determine the dimension of the space of homogeneous polynomials of a fixed degree vanishing at finitely many points in the projective plane to certain multiplicities. We present various aspects of this problem and a…

We construct a new representation for two- and three-point correlators of operators from sl(2) sector of planar N = 4 SYM. The spin and twist of operators are arbitrary. We start with the correlation function of light-ray operators and…

A Gelfan'd--Dyson mapping is used to generate a one-boson realization for the non-standard quantum deformation of $sl(2,\R)$ which directly provides its infinite and finite dimensional irreducible representations. Tensor product…

A class of second order difference (discrete) operators with a partial algebraization of the spectrum is introduced. The eigenfuncions of the algebraized part of the spectrum are polinomials (discrete polinomials). Such difference operators…

As is well-known, poly-Bernoulli polynomials are defined in terms of polylogarithm functions. Recently, as degenerate version of such functions and polynomials, degenerate polylogarithm functions were introduced and degenertae…

Any homogeneous polynomial $P(x, y, z)$ of degree $d$, being restricted to a unit sphere $S^2$, admits essentially a unique representation of the form $\lambda_0 + \sum_{k = 1}^d \lambda_k [\prod_{j = 1}^k L_{kj}]$, where $L_{kj}$'s are…

Let $M_\phi$ be a surface bundle over a circle with monodromy $\phi:S \rightarrow S$. We study deformations of certain reducible representations of $\pi_1(M_\phi)$ into $\text{SL}(n,\mathbb{C})$, obtained by composing a reducible…

We characterize all linear operators on finite or infinite-dimensional spaces of univariate real polynomials preserving the sets of elliptic, positive, and non-negative polynomials, respectively. This is done by means of Fischer-Fock…

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 introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on underlying polynomial Heisenberg algebras and their defining…

In this thesis quadratic and cubic algebras, which are extensions of SU(1,1) and SU(2) are studied in detail, with particular attention being given to their construction, their finite and infinite dimensional irreducible representations and…

For monomial special multiserial algebras, which in general are of wild representation type, we construct radical embeddings into algebras of finite representation type. As a consequence, we show that the representation dimension of…

We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…

We study the representations of a class of non-commutative polynomial algebras truncated at degree 3, with one additional relation. We determine the irreducible components of their varieties of representations. We do this by showing that…