Related papers: Row and column detection complexities of character…
Within the AdS/CFT correspondence, computational complexity for reduced density matrices of holographic conformal field theories has been conjectured to be related to certain geometric observables in the dual gravity theory. We study this…
In standard clustering problems, data points are represented by vectors, and by stacking them together, one forms a data matrix with row or column cluster structure. In this paper, we consider a class of binary matrices, arising in many…
Let $k$ be a field containing an algebraically closed field of characteristic zero. If $G$ is a finite group and $D$ is a division algebra over $k$, finite dimensional over its center, we can associate to a faithful $G$-grading on $D$ a…
This paper exhibits a series of semantic characterisations of sublinear nondeterministic complexity classes. These results fall into the general domain of logic-based approaches to complexity theory and so-called implicit computational…
Let $G$ be a finite group, and let ${\rm{cd}}(G)$ denote the set of degrees of the irreducible complex characters of $G$. Define then the character degree graph $\Delta(G)$ as the (simple undirected) graph whose vertices are the prime…
This survey article is concerned with the modeling of the kinematical structure of quantum systems in an algebraic framework which eliminates certain conceptual and computational difficulties of the conventional approaches. Relying on the…
Let g be a simple Lie algebra. We consider the category O-hat of those modules over the affine quantum group Uq(g-hat) whose Uq(g)-weights have finite multiplicity and lie in a finite union of cones generated by negative roots. We show that…
We investigate the existence of heavy columns in binary matrices with distinct rows. A column of an m x n binary matrix is called heavy if the number of ones in it is at least m/2. We introduce two recursive algorithms, A1 and A2, that…
The theory of representations of a crossed module is a direct generalization of the theory of representations of groups. For a finite group G, the Drinfeld quantum double of the group G is a Hopf algebra that represents a special case of…
These notes are our contribution to the Proceedings of the ICM 2026. We discuss some results we have obtained (in part jointly with coauthors) regarding the representation theory of reductive algebraic groups over algebraically closed…
Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph…
Network science has presented community detection as a valuable tool for revealing functional modules in complex systems rooted in the wiring architectures of complex networks. The varying procedures of community detection can produce,…
The notion of quantized characters is introduced in our previous paper as a natural quantization of characters in the context of asymptotic representation theory for compact quantum groups. As in the case of ordinary groups, the…
The classification of irreducible, spherical characters of the infinite-dimensional unitary/orthogonal/symplectic groups can be obtained by finding all possible limits of normalized, irreducible characters of the corresponding…
In this paper, we considered the theory of quasideterminants and row and column determinants. We considered the application of this theory to the solving of a system of linear equations in quaternion algebra. We established correspondence…
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
In this note, we introduce a new concept of a {\it generalized algebraic rational identity} to investigate the structure of division rings. The main theorem asserts that if a non-central subnormal subgroup $N$ of the multiplicative group…
Conjunctive table algebras are introduced and axiomatically characterized. A conjunctive table algebra is a variant of SPJR algebra (a weaker form of relational algebra), which corresponds to conjunctive queries with equality. The table…
Motivated by chemical applications, we revisit and extend a family of positive definite kernels for graphs based on the detection of common subtrees, initially proposed by Ramon et al. (2003). We propose new kernels with a parameter to…