Related papers: Embedding the flag representation in divided power…

A representation embedding between cartesian theories can be defined to be a functor between respective categories of models that preserves finitely-generated projective models and that preserves and reflects certain epimorphisms. This…

We study generalizations of Schur functors from categories consisting of flags of vector spaces. We give different descriptions of the category of such functors in terms of representations of certain combinatorial categories and infinite…

It is known that graphs cellularly embedded into surfaces are equivalent to ribbon graphs. In this work, we generalize this statement to broader classes of graphs and surfaces. Half-edge graphs extend abstract graphs and are useful in…

We establish a number of results which say, roughly, that interpretation functors preserve algebraic complexity. First we show that representation embeddings between categories of modules of finite-dimensional algebras induce embeddings of…

We introduce a novel embedding method diverging from conventional approaches by operating within function spaces of finite dimension rather than finite vector space, thus departing significantly from standard knowledge graph embedding…

This paper defines, for each graph $G$, a flag vector $fG$. The flag vectors of the graphs on $n$ vertices span a space whose dimension is $p(n)$, the number of partitions on $n$. The analogy with convex polytopes indicates that the linear…

The first part of the paper centers in the study of embeddability between partially commutative groups. In [KK], for a finite simplicial graph $\Gamma$, the authors introduce an infinite, locally infinite graph $\Gamma^e$, called the…

This paper defines for each object $X$ that can be constructed out of a finite number of vertices and cells a vector $fX$ lying in a finite dimensional vector space. This is the flag vector of $X$. It is hoped that the quantum topological…

In this article we study the representations of general linear groups which arise from their action on flag spaces. These representations can be decomposed into irreducibles by proving that the associated Hecke algebra is cellular. We give…

Knowledge graph embeddings are now a widely adopted approach to knowledge representation in which entities and relationships are embedded in vector spaces. In this chapter, we introduce the reader to the concept of knowledge graph…

We classify all products of flag varieties with finitely many orbits under the diagonal action of the general linear group. We also classify the orbits in each case and construct explicit representatives. This generalizes the classical…

We define the class of admissible linear embeddings of flag varieties. The definition is given in the general language of algebraic geometry. We then prove that an admissible linear embedding of flag varieties has a certain explicit form in…

In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…

We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of finite-dimensional modules over any…

The concept of F-algebra and its representation can be extended to an arbitrary bundle. We define operations of fibered F-algebra in fiber. The paper presents the representation theory of of fibered F-algebra as well as a comparison of…

We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.

We introduce loop spaces (in the sense of derived algebraic geometry) into the representation theory of reductive groups. In particular, we apply the theory developed in our previous paper arXiv:1002.3636 to flag varieties, and obtain new…

Vector representations of graphs and relational structures, whether hand-crafted feature vectors or learned representations, enable us to apply standard data analysis and machine learning techniques to the structures. A wide range of…

Graph embeddings deal with injective maps from a given simple, undirected graph $G=(V,E)$ into a metric space, such as $\mathbb{R}^n$ with the Euclidean metric. This concept is widely studied in computer science, see \cite{ge1}, but also…

This work provides the first unifying theoretical framework for node (positional) embeddings and structural graph representations, bridging methods like matrix factorization and graph neural networks. Using invariant theory, we show that…