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Transversal structures (also known as regular edge labelings) are combinatorial structures defined over 4-connected plane triangulations with quadrangular outer-face. They have been intensively studied and used for many applications…
Representations of Spin groups and Clifford algebras derived from the structure of qubit trees are introduced in this work. For ternary trees the construction is more general and reduction to binary trees is formally defined by deletion of…
We re-examine some topics in representation theory of Lie algebras and Springer theory in a more general context, viewing the universal enveloping algebra as an example of the section ring of a quantization of a conical symplectic…
Local distinguishability of orthogonal product states is an area of active research in quantum information theory. However, most of the relevant results about local distinguishability found in bipartite quantum systems and very few are…
The present paper is devoted to study multi-dimensional coupled FBSDEs with diagonally quadratic generators. Relying on a comparison result obtained in [20], we provide conditions under which there exists a global solution. As a byproduct,…
We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and…
In recent years, various nonlinear algebraic structures have been obtained in the context of quantum systems as symmetry algebras, Painlev\'{e} transcendent models and missing label problems. In this paper we treat all of these algebras as…
The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…
We introduce a generalization of bivariate Griffiths polynomials depending on an additional parameter $\lambda$. These $\lambda$-Griffiths polynomials are bivariate, bispectral and biorthogonal. For two specific values of the parameter…
The idea of orthogonal polynomials has been generalized in two ways to achieve new types of polynomials: noncommutative orthogonal polynomials and biorthogonal polynomials. This paper brings these two different generalizations together to…
We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper…
We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. The category of…
Linear constraint systems (LCS) have proven to be a surprisingly prolific tool in the study of non-classical correlations and various related issues in quantum foundations. Many results are known for the Boolean case, yet the generalisation…
We investigate the quantum nonlocality via the discrimination on two, three and four-qubit orthogonal product bases (OPBs). We show that every two-qubit, and some three and four-qubit OPBs can be locally distinguished. It turns out that the…
In this paper we establish the principal bundle counterpart of the well-known and widely applied notion of vector bundle groupoid (VB-groupoid). In particular, we provide a general notion of principal bundle groupoid (PB-groupoid) as a…
Springer resolution of the set of nilpotent elements in a semisimple Lie algebra plays a central role in geometric representation theory. A new structure on this variety has arisen in several representation theoretic constructions, such as…
In this paper, we first discuss the relation between VB-Courant algebroids and E-Courant algebroids and construct some examples of E-Courant algebroids. Then we introduce the notion of a generalized complex structure on an E-Courant…
We find a family of convergent schemes of nodes for non-complete interpolatory quadrature rules.
Koornwinder polynomials are a 6-parameter BC_n-symmetric family of Laurent polynomials indexed by partitions, from which Macdonald polynomials can be recovered in suitable limits of the parameters. As in the Macdonald polynomial case,…
We introduce the concept of braided noncommutative Poisson bialgebras. The theory of cocycle bicrossproducts for noncommutative Poisson bialgebras is developed. As an application, we solve the extending problem by using some non-abelian…