Related papers: Layer structure of irreducible Lie algebra modules

It is known that characters of irreducible representations of finite Lie algebras can be obtained using theWeyl character formula including Weyl group summations which make actual calculations almost impossible except for a few Lie algebras…

We discover a large class of simple affine vertex algebras $V_{k} (\mathfrak g)$, associated to basic Lie superalgebras $\mathfrak g$ at non-admissible collapsing levels $k$, having exactly one irreducible $\mathfrak g$-locally finite…

Let $L$ be a finite-dimensional Lie algebra over a field of non-zero characteristic and let $S$ be a subalgebra. Suppose that $X$ is a finite set of finite-dimensional $L$-modules. Let $D$ be the category of all finite-dimensional…

Let $g$ be a finite dimensional simple Lie algebra. Denote by $\mathcal B$ the category of all bounded weight $g$-modules, i.e. those which are direct sum of their weight spaces and have uniformly bounded weight multiplicities. A result of…

The problem of computing the characters of the finite dimensional irreducible representations of the Lie superalgebra $\mathfrak{gl}(m|n)$ over $\C$ was solved a few years ago by V. Serganova. In this article, we present an entirely…

We investigate the representations of the hyperalgebras associated to the map algebras $\mathfrak g\otimes \mathcal A$, where $\mathfrak g$ is any finite-dimensional complex simple Lie algebra and $\mathcal A$ is any associative commutative…

We give a combinatorial formula for the character of a finite-dimensional irreducible representation of the periplectic Lie superalgebra $\mathfrak{p}(n)$. The character of irreducible module $L(\mu)$ is given by a cancellation-free…

The paper explores the indecomposable submodule structures of quantum divided power algebra $\mathcal{A}_q(n)$ defined in \cite{HU} and its truncated objects $\mathcal{A}_q(n, \bold m)$. An "intertwinedly-lifting" method is established to…

In this paper, we classify irreducible modules for loop extended Witt algebras with finite dimensional weight spaces. They turn out to be either modules with uniformly bounded weight spaces or highest weight modules. We further prove that…

The level-$1$ integrable highest weight modules of $U_q(\widehat{sl}_2)$ admit a level-$0$ action of the same algebra. This action is defined using the affine Hecke algebra and the basis of the level-$1$ module generated by components of…

In this paper, as the first step towards classification of simple weight modules with finite dimensional weight spaces over Witt algebras $W_n$, we explicitly describe supports of such modules. We also obtain some descriptions on the…

Let g_A (respectively, g_A(\mu)) be the graded multi-loop Lie algebra (respectively graded twisted multi-loop Lie algebra)" associated with the simple finite dimensional Lie algebra g over the complex field C. In this paper, we prove that…

Suppose $g=g_0+g_1$ is a finite-dimensional restricted Lie superalgebra over an algebraically closed field $k$ of characteristic $p>2$. In this article, we propose a conjecture for maximal dimensions of irreducible modules over the…

We classify irreducible finite-dimensional modules of a collection of real Lie superalgebras that includes the simple ones, their classical variants, complex Lie superalgebras after restriction of scalars, and all real Lie algebras. Our…

Let $\mathbb K$ be an algebraically closed field of characteristic zero, $A = \mathbb K[x_1,\dots,x_n]$ the polynomial ring, and let $W_n(\mathbb K)$ denote the Lie algebra of all $\mathbb K$-derivations on $A$. The Lie algebra $W_n :=…

This work provides the first step toward the classification of irreducible finite weight modules over twisted affine Lie superalgebras. We study all such modules whether the canonical central element acts as a nonzero multiple of the…

The multiplicity of a weight in a finite-dimensional irreducible representation of a simple Lie algebra g can be computed via Kostant's weight multiplicity formula. This formula consists of an alternating sum over the Weyl group (a finite…

Let $\mathfrak{g}$ be a simple finite dimensional complex Lie algebra and let $\widehat{\mathfrak{g}}$ be the corresponding affine Lie algebra. Kac and Wakimoto observed that in some cases the coefficients in the character formula for a…

We study the representations of a class of non-commutative polynomial algebras truncated at degree 3, with one additional relation. We determine the irreducible components of their varieties of representations. We do this by showing that…

To a finite dimensional representation of a complex Lie group $G$, an associative algebra of adjoint covariant polynomial maps from the direct sum of $m$ copies of the Lie algebra $\mathfrak{g}$ of $G$ into an algebra of complex matrices is…