Related papers: Central elements in the universal enveloping algeb…

The construction of a generic representation of $g\ell(n+1)$ or of the trigonomentric deformation of its enveloping algebra known as algebraic induction is conveniently formulated in term of Lax matrices. The Lax matrix of the constructed…

Let $\widetilde{\mathcal U}_{\mathbb Z}({\widehat{\frak{gl}}_n})$ be the Garland integral form of ${\mathcal U}(\widehat{{\frak{gl}}}_n)$ introduced by Garland \cite{Ga}, where ${\mathcal U}(\widehat{{\frak{gl}}}_n)$ is the universal…

For quantized universal enveloping algebras we construct weight modules by inducing representations of the centralizer of the Cartan subalgebra in the quantized universal enveloping algebra. The induced modules arising from…

One of the central questions in theoretical particle physics, since already several decades, has been that of "masses and mixings of the quarks. With the entry of neutrino oscillations into the field, the issue of lepton masses has added a…

We develop a representation theory approach to the study of generalized hypergeometric functions of Gelfand, Kapranov and Zelevisnky (GKZ). We show that the GKZ hypergeometric functions may be identified with matrix elements of…

In this short note we study the center of the universal enveloping algebra of the strange Lie superalgebra Q(N). We obtain an analogue of the well known Perelomov-Popov formula (1968) for central elements of this algebra - an expression of…

Let $G$ be a finite group and $N$ be a normal subgroup of $G$. Let $J=J(F[N])$ denote the Jacboson radical of $F[N]$ and $I={\rm Ann}(J)=\{\alpha \in F[G]|J\alpha =0\}$. We have another algebra $F[G]/I$. We study the decomposition of Cartan…

General properties of ternary semigroups and groups are considered. The bi-element representation theory in which every representation matrix corresponds to a pair of elements is built, connection with the standard theory is considered and…

Let $\mathfrak{g}$ and $\mathfrak{h}$ be two Lie algebras with $\mathfrak{h}$ finite dimensional and consider ${\mathcal A} = {\mathcal A} (\mathfrak{h}, \, \mathfrak{g})$ to be the corresponding universal algebra as introduced in…

In many physical problems or applications one has to study functions that are invariant under the action of a symmetry group G and this is best done in the orbit space of G if one knows the equations and inequalities defining the orbit…

We construct a universal continuous invariant bilinear form for the Lie algebra of compactly supported sections of a Lie algebra bundle in a topological sense. Moreover we construct a universal continuous central extension of a current…

The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…

Permutation invariant polynomial functions of matrices have previously been studied as the observables in matrix models invariant under $S_N$, the symmetric group of all permutations of $N$ objects. In this paper, the permutation invariant…

In this paper, we consider a special class of Capelli bitableaux, namely the Capelli-Deruyts bitableaux. The main results we prove are the hook coefficient lemma and the expansion theorem. Capelli-Deruyts bitableaux of rectangular shape are…

We define the notion of an invariant function on a cluster ensemble with respect to an action of the cluster modular group on its associated function fields. We realize many examples of previously studied functions as elements of this type…

The Laguerre functions constitute one of the fundamental basis sets for calculations in atomic and molecular electron-structure theory, with applications in hadronic and nuclear theory as well. While similar in form to the Coulomb…

The set of all centralizers of elements in a finite group $G$ is denoted by $Cent(G)$ and $G$ is called $n-$centralizer if $|Cent(G)| = n$. In this paper, the structure of centralizers in a non-abelian finite group $G$ with this property…

Let $\gg$ be a simple, finite-dimensional complex Lie algebra, and let $V^k(\gg)$ denote the universal affine vertex algebra associated to $\gg$ at level $k$. The Cartan involution on $\gg$ lifts to an involution on $V^k(\gg)$, and we…

The derivation of absolute (moduli-independent) U-invariants for all N>2 extended supergravities at D=4 in terms of (moduli-dependent) central and matter charges is reported. These invariants give a general definition of the ``topological''…

We describe the double Yangian of the general linear Lie algebra $\mathfrak{gl}_N$ by following a general scheme of Drinfeld. This description is based on the construction of the universal $R$-matrix for the Yangian. To make the exposition…