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We study the degree of irreducible morphisms in any Auslander-Reiten component of a finite dimensional algebra over an algebraically closed field. We give a characterization for an irreducible morphism to have finite left (or right) degree.…

In this article, we review some aspects of logarithmic conformal field theories which can be inferred from the characters of irreducible submodules of indecomposable modules. We will mainly consider the W(2,2p-1,2p-1,2p-1) series of triplet…

For the algebra L= K <x, d/dx, \int> of polynomial integro-differential operators over a field K of characteristic zero, a classification of indecomposable, generalized weight L-modules of finite length is given. Each such module is an…

We investigate the representations of the exotic conformal Galilei algebra. This is done by explicitly constructing all singular vectors within the Verma modules, and then deducing irreducibility of the associated highest weight quotient…

We prove a highest weight theorem classifying irerducible finite--dimensional representations of quantum affine algebras and survey what is currently known about the structure of these representations.

We construct large families of simple modules for untwisted affine Lie algebras using induction from one-dimensional modules over nilpotent loop subalgebras. We also show that the vector space of the first self-extensions for these module…

Singular vectors of a representation of a finite-dimensional simple Lie algebra are weight vectors in the underlying module that are nullified by positive root vectors. In this article, we use partial differential equations to find all the…

We provide a classification and explicit bases of tableaux of all irreducible generic Gelfand-Tsetlin modules for the Lie algebra $\mathfrak{gl}(n)$.

Let $L(-{1/2}(l+1),0)$ be the simple vertex operator algebra associated to an affine Lie algebra of type $A_{l}^{(1)}$ with the lowest admissible half-integer level $-{1/2}(l+1)$, for even l. We study the category of weak modules for that…

In this paper, we first present a classification theorem of infinite-dimensional simple Novikov algebras over an algebraically closed field with characteristic 0. Then we classify all the irreducible modules of a certain…

In this article we construct a new class of finite dimensional irreducible modules genaralizing evaluation modules for multiloop superalgebra of type A(m,n) and C(m). We prove that these are the only such modules. In all other cases it is…

We study the homotopy category $ K(\Inj A)$ of all injective modules over a finite dimensional algebra $A$ with discrete derived category. We give a classification of the indecomposable objects of $ K(\Inj A)$ for any radical square zero…

In this work, we construct some irreducible components of the space of two-dimensional holomorphic foliations on $\mathbb{P}^n$ associated to some algebraic representations of the affine Lie algebra $\mathfrak{aff}(\mathbb{C})$. We give a…

We prove that an irreducible quasifinite module over the central extension of the Lie algebra of $N\times N$-matrix differential operators on the circle is either a highest or lowest weight module or else a module of the intermediate…

In this note we give an explicit description of the irreducible components of the reduced point varieties of quantum polynomial algebras.

We complete the classification of the finite dimensional irreducible representations of finite W-algebras associated to even multiplicity nilpotent elements in classical Lie algebras. This extends earlier work where this classification is…

For a weighted graph $E$, we construct representation graphs $F$, and consequently, $L_K(E)$-modules $V_F$, where $L_K(E)$ is the Leavitt path algebra associated to $E$, with coefficients in a field $K$. We characterise representation…

In this paper we classify and give Kazhdan-Lusztig type character formulas for equivariantly irreducible representations of Lie algebras of reductive algebraic groups over a field of large positive characteristic. The equivariance is with…

We consider a category of modules that admit compatible actions of the commutative algebra of Laurent polynomials and the Lie algebra of divergence zero vector fields on a torus and have a weight decomposition with finite dimensional weight…

We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification of the irreducible representations, the construction of the Weyl modules, base change,…