Related papers: Representations of posets: Linear versus Unitary

Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…

The first steps towards linearisation of partial orders and equivalence relations are described. The definitions of partial orders and equivalence relations (on sets) are formulated in a way that is standard in category theory and that…

We introduce partially ordered sets (posets) with an additional structure given by a collection of vector subspaces of an algebra $A$. We call them algebraically equipped posets. Some particular cases of these, are generalized equipped…

We describe and analyze different approaches to represent ordinal patterns. All of these can be found in the literature. The most important representations (plus sub-classes) are compared in terms of their applicability from different…

We shall discuss how the notions of multicategories and their linear representations are related with tensor categories. When one focuses on the ones arizing from planar diagrams, it particularly implies that there is a natural one-to-one…

In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…

We describe all weights which are appropriated for the unitarization of linear representations of primitive partially ordered sets of finite type.

In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…

Several advances have extended the power and versatility of coherent state theory to the extent that it has become a vital tool in the representation theory of Lie groups and their Lie algebras. Representative applications are reviewed and…

We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of…

This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…

A binary relation defined on a poset is a weakening relation if the partial order acts as a both-sided compositional identity. This is motivated by the weakening rule in sequent calculi and closely related to models of relevance logic. For…

Lie conformal algebras appear in the theory of vertex algebras. Their relation is similar to that of Lie algebras and their universal enveloping algebras. Associative conformal algebras play a role in conformal representation theory. We…

Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…

A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices…

The results here presented are a continuation of the algebraic research line which attempts to find properties of multiple-valued systems based on a poset of two agents. The aim of this paper is to exhibit two relationships between some…

This paper continues the study of the poset of eigenspaces of elements of a unitary reflection group (for a fixed eigenvalue), which was commenced in [6] and [5]. The emphasis in this paper is on the representation theory of unitary…

Every partial applicative structure gives rise to an indexed binary relation, that is a contravariant functor from the category of sets to the category of sets endowed with binary relations and maps preserving them. In this paper we…

Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…

We classify the automorphic representations (over number fields) and the irreducible admissible representations (over local fields) of unitary groups which are not quasi-split, under the assumption that the same is known for quasi-split…