Related papers: Linear versus set valued Kronecker representations
The distributed representations currently used are dense and uninterpretable, leading to interpretations that themselves are relative, overcomplete, and hard to interpret. We propose a method that transforms these word vectors into reduced…
We introduce the notion of a super-representation of a quiver. For super-representations of quivers over a field of characteristic zero, we describe the corresponding (super)algebras of polynomial semi-invariants and polynomial invariants.
In this paper, we propose a set theoretic approach for knowledge representation. While the syntax of an application domain is captured by set theoretic constructs including individuals, concepts and operators, knowledge is formalized by…
A subspace representation of a poset $\mathcal S=\{s_1,...,s_t\}$ is given by a system $(V;V_1,...,V_t)$ consisting of a vector space $V$ and its subspaces $V_i$ such that $V_i\subseteq V_j$ if $s_i \prec s_j$. For each real-valued vector…
A correspondence functor is a functor from the category of finite sets and correspondences to the category of $k$-modules, where $k$ is a commutative ring. We determine exactly which simple correspondence functors are projective. Moreover,…
We introduce thread quivers as an (infinite) generalization of quivers, and show that every k-linear (k algebraically closed) hereditary category with Serre duality and enough projectives is equivalent to the category of finitely presented…
We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is…
We consider a group SO(2n+1) over a p-adic field, and tempered irreducible representations of this group, of unipotent reduction. We use the construction due to Lusztig of these representations. In an old paper with Moeglin, we have defined…
A numeric function $\rho$: $\rho(k)=1+\frac{k-1}{k+1}, k \in N$ was considered in [1]. In its terms criterions of finite representability and tameness of marked quivers, posets with equivalence and dyadic posets can be obtained; Dynkin…
The first half of this dissertation reviews the basic notion of vector-valued modular forms and its connection to differential equations. The main purpose of the dissertation is to classify spaces of vector-valued modular forms associated…
Multisorted modules, equivalently representations of quivers, equivalently additive functors on preadditive categories, encompass a wide variety of additive structures. In addition, every module has a natural and useful multisorted…
We study maximum antichains in two posets related to quiver representations. Firstly, we consider the set of isomorphism classes of indecomposable representations ordered by inclusion. For various orientations of the Dynkin diagram of type…
We will give quiver presentations of the Grothendieck constructions of functors from a small category to the 2-category of $\Bbbk$-categories for a commutative ring $\Bbbk$.
In the case of Dynkin quivers we establish a formula for the Grothendieck class of a quiver cycle as the iterated residue of a certain rational function, for which we provide an explicit combinatorial construction. Moreover, we utilize a…
An integer sequence that is defined by initial values and a linear recurrence with constant integer coefficients, can be represented by the difference of two arithmetic terms containing exponentiation. All constants occuring in the term are…
It is shown that certain transformations on quiver-dimension vector pairs induce isomorphisms on the corresponding moduli spaces of quiver representations and map a stable dimension vector to a stable dimension vector. This result combined…
We introduce the notion of the full quiver of a representation of an algebra, which is a cover of the (classical) quiver, but which captures properties of the representation itself. Gluing of vertices and of arrows enables one to study…
In the field of natural language processing (NLP), continuous vector representations are crucial for capturing the semantic meanings of individual words. Yet, when it comes to the representations of sets of words, the conventional…
The reduced Kronecker coefficients are particular instances of Kronecker coefficients that contain enough information to recover them. In this notes we compute the generating function of a family of reduced Kronecker coefficients. We also…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…