Related papers: Reducibility of self-adjoint linear relations and …

The classical concept of $Q$-functions associated to symmetric and selfadjoint operators due to M.G. Krein and H. Langer is extended in such a way that the Dirichlet-to-Neumann map in the theory of elliptic differential equations can be…

Various properties of a class of braid matrices, presented before, are studied considering $N^2 \times N^2 (N=3,4,...)$ vector representations for two subclasses. For $q=1$ the matrices are nontrivial. Triangularity $(\hat R^2 =I)$…

By exploiting the connection between solving algebraic $\top$-Riccati equations and computing certain deflating subspaces of $\top$-palindromic matrix pencils, we obtain theoretical and computational results on both problems. Theoretically,…

After having established elementary results on the relationship between a finite complex (pseudo-)reflection group W < GL(V) and its reflection arrangement A, we prove that the action of W on A is canonically related with other natural…

We study functions defined on the vertices of the Hamming graphs $H(n,q)$. The adjacency matrix of $H(n,q)$ has $n+1$ distinct eigenvalues $n(q-1)-q\cdot i$ with corresponding eigenspaces $U_{i}(n,q)$ for $0\leq i\leq n$. In this work, we…

We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly…

For every multivariable polynomial $p$, with $p(0)=1$, we construct a determinantal representation $$p=\det (I - K Z),$$ where $Z$ is a diagonal matrix with coordinate variables on the diagonal and $K$ is a complex square matrix. Such a…

Let $K[HK_{\Theta}]$ denote the Hecke-Kiselman algebra of a finite oriented graph $\Theta$ over an algebraically closed field $K$. All irreducible representations, and the corresponding maximal ideals of $K[HK_{\Theta}]$, are characterized…

Let $U_q(\hat{\cal G})$ be an infinite-dimensional quantum affine Lie algebra. A family of central elements or Casimir invariants are constructed and their eigenvalues computed in any integrable irreducible highest weight representation.…

We study families of self-adjoint operators with given spectra whose sum is a scalar operator. Such families are $*$-representations of certain algebras which can be described in terms of graphs and positive functions on them. The main…

A linear operator on a Hilbert space $\mathbb{H}$, in the classical approach of von Neumann, must be symmetric to guarantee self-adjointness. However, it can be shown that the symmetry could be ommited by using a criterion for the graph of…

We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r)…

Let T be an involution of the finite dimensional complex reductive Lie algebra g and g=k+p be the associated Cartan decomposition. Denote by K the adjoint group of k. The K-module p is the union of the subsets p^{(m)}={x | dim K.x =m},…

Two one-parameter families of twists providing kappa-Minkowski * -product deformed spacetime are considered: Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two perspectives. The first one is the Hopf module…

The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…

As a generalization of vertex connectivity, for connected graphs $G$ and $T$, the $T$-structure connectivity $\kappa(G, T)$ (resp. $T$-substructure connectivity $\kappa^{s}(G, T)$) of $G$ is the minimum cardinality of a set of subgraphs $F$…

Let $G$ be a connected reductive affine algebraic group defined over the complex numbers, and $K\subset G$ be a maximal compact subgroup. Let $X , Y$ be irreducible smooth complex projective varieties and $f: X \rightarrow Y$ an algebraic…

The Nevanlinna matrix of a half-line Jacobi operator coincides, up to multiplication with a constant matrix, with the monodromy matrix of an associated canonical system. This canonical system is discrete in a certain sense, and is…

To facilitate a simultaneous treatment of an arbitrary number of colors in representation theory-based descriptions of QCD color structure, we derive an $N$-independent reduction of SU($N$) tensor products. To this end, we label each…

The Jacobian elliptic functions are generalized and applied to a nonlinear eigenvalue problem with $p$-Laplacian. The eigenvalue and the corresponding eigenfunction are represented in terms of common parameters, and a complete description…