Related papers: On the unitarization of linear representations of …
We prove that partially ordered set has finite number of finite-dimensional indecomposable nonequivalent Hilbert representations with orthoscalarity condition if and anly if it has finite number of indecomposable linear representations. We…
We begin a systematic study of unitary representations of minimal $W$-algebras. In particular, we classify unitary minimal $W$-algebras and make substantial progress in classification of their unitary irreducible highest weight modules. We…
The main purpose of this work is to review the results obtained recently concerning the unitarization of highest weight representations for affine Kac-Moody algebras following the work of Jakobsen and Kac.
A number of recent papers treated the representation theory of partially ordered sets in unitary spaces with the so called orthoscalar relation. Such theory generalizes the classical theory which studies the representations of partially…
This paper focuses on the specification of the weights for the components of mixture priors.
We obtain a complete classification of minimal simple unitary $W$-algebras.
The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately…
In this paper, we study several definitions of generalized rank weights for arbitrary finite extensions of fields. We prove that all these definitions coincide, generalizing known results for extensions of finite fields.
We present a uniform description of sets of $m$ linear forms in $n$ variables over the field of rational numbers whose computation requires $m(n - 1)$ additions.
We characterize unitary representations of braid groups $B_n$ of degree linear in $n$ and finite images of such representations of degree exponential in $n$.
We study unitarity of lowest weight irreducible representations of rational Cherednik algebras. We prove several general results, and use them to determine which lowest weight representations are unitary in a number of cases. In particular,…
In a recent paper ([1],[2]) we have classified explicitely all the unitary highest weight representations of non compact real forms of semisimple Lie Algebras on Hermitian symmetric space. These results are necessary in order to construct…
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…
In this paper, we continue the study of linear sets with complementary weights. We find criteria to determine the set of points of any fixed weight and use this to present particular linear sets with few points of weight more than one. We…
We classify unital associative conformal algebras of linear growth and provide new examples of such.
Using Jakobsen theorems, unitarizability in Hermitian Symmetric Spaces is discussed. The set of all missing highest weights is explicitly calculated and the construction of their corresponding highest weights vectors is studied.
We characterize finite-dimensional thick representations over ${\Bbb C}$ of connected complex semi-simple Lie groups by irreducible representations which are weight multiplicity-free and whose weight posets are totally ordered sets.…
In this paper, we discuss the generalized Hamming weights of a class of linear codes associated with non-degenerate quadratic forms. In order to do so, we study the quadratic forms over subspaces of finite field and obtain some interesting…
The purpose of this paper is to study stable representations of partially ordered sets (posets) and compare it to the well known theory for quivers. In particular, we prove that every indecomposable representation of a poset of finite type…
The generalized Hamming weights of a linear code have been extensively studied since Wei first use them to characterize the cryptography performance of a linear code over the wire-tap channel of type II. In this paper, we investigate the…