Related papers: The classification of thick representations of sim…

We study the irreducible complex representations of general linear groups over principal ideal local rings of length two with a fixed finite residue field. We construct a canonical correspondence between the irreducible representations of…

There are studied Lie groups considered as almost hypercomplex Hermitian-Norden manifolds, which are integrable and have the lowest dimension four. It is established a correspondence of the derived Lie algebras of types of invariant…

We show that the classification of simple finite group schemes over an algebraically closed field reduces to the classification of abstract simple finite groups and of simple restricted Lie algebras in positive characteristic. Both these…

We describe all irreducible conformal subalgebras of Cend_N. The classification of simple and semisimple associative conformal algebras with finite faithful representation follows from this description.

Given F a locally compact, non-discrete, non-archimedean field of characteristic different from 2 and R an integral domain such that a non-trivial smooth F-character with values in the multiplicative group of R exists, we construct the…

This paper introduces calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The primary technique is to provide indexing sets for controlling the…

This paper describes finite dimensionall irreducible representations of both twisted and untwisted Cartan map Lie superalgebras.

We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness…

We classify the quasifinite highest weight modules over a family of subalgebras W_{\infty}^{n} of the central extension W_{1+\infty} of the Lie algebra of differential operators on the circle consisting of operators of order \geq n. We…

In the present paper we classify all irreducible continuous representations of the simple linearly compact n-Lie superalgebra of type S. The classification is based on a bijective correspondence between the continuous representations of the…

Object of investigation are almost hypercomplex manifolds with Hermitian-Norden metrics of the lowest dimension. The considered manifolds are constructed on 4-dimensional Lie groups. It is established a relation between the classes of a…

We prove that all linear Lie groups satisfying the conditions listed in the title are finite extensions of commutative Lie groups.

Let G be the real points of a simply connected, semisimple, simply laced complex Lie group, and let \tilde{G} be the nonlinear double cover of G. We discuss a set of small genuine irreducible representations of \tilde{G} which can be…

In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…

We construct every finite-dimensional irreducible representation of the simple Lie algebra of type $\mathsf{E}_{7}$ whose highest weight is a nonnegative integer multiple of the dominant minuscule weight associated with the type…

We classify the simple quantum group modules with finite dimensional weight spaces when the quantum parameter $q$ is transcendental and the Lie algebra is not of type $G_2$. This is part $2$ of the story. The first part being Irreducible…

Irreducible nonzero level modules with finite-dimensional weight spaces are studied for non-twisted affine Lie superalgebras. A complete classification is obtained for superalgebras A(m,n)^ and C(n)^. In other cases the classification…

A bivariate representation of a complex simple Lie algebra is an irreducible representation having highest weight a combination of the first two fundamental weights. For a complex classical Lie algebra, we establish an expression for the…

We prove that an abstract (possibly infinite dimensional) complex irreducible representation of a discrete supersolvable group is monomial if and only if it has finite weight. We also prove a general result that implies converse of Schur's…

We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called weakly maximal representations. They are defined in terms of invariants in bounded cohomology and extend considerably the…