Related papers: Representations of Lie superalgebras with fusion f…

We study the category of finite--dimensional bi--graded representations of toroidal current algebras associated to finite--dimensional complex simple Lie algebras. Using the theory of graded representations for current algebras, we…

Motivated by the theory of unitary representations of finite dimensional Lie supergroups, we describe those Lie superalgebras which have a faithful finite dimensional unitary representation. We call these Lie superalgebras unitary. This is…

We investigate the category of finite-dimensional representations of twisted hyper loop algebras, i.e., the hyperalgebras associated to twisted loop algebras over finite-dimensional simple Lie algebras. The main results are the…

We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the…

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…

We consider typical finite dimensional complex irreducible representations of a basic classical simple Lie superalgebra, and give a sufficient condition on when unique factorization of finite tensor products of such representations hold. We…

We give a complete description of the finite-dimensional irreducible representations of the Yangian associated with the orthosymplectic Lie superalgebra $\frak{osp}_{1|2}$. The representations are parameterized by monic polynomials in one…

We classify the finite-dimensional irreducible representations of the super Yangian associated with the orthosymplectic Lie superalgebra ${\frak osp}_{2|2n}$. The classification is given in terms of the highest weights and Drinfeld…

We survey some important results concerning the finite--dimensional representations of the loop algebra of a simple complex Lie algebra, and their twisted loop subalgebras. In particular, we review the parametrization and description of the…

We define global and local Weyl modules for Lie superalgebras of the form $\mathfrak{g} \otimes A$, where $A$ is an associative commutative unital $\mathbb{C}$-algebra and $\mathfrak{g}$ is a basic Lie superalgebra or $\mathfrak{sl}(n,n)$,…

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,…

In this paper we determine the projective unitary representations of finite dimensional Lie supergroups whose underlying Lie superalgebra is $\frak{g} = A \otimes \frak{k}$, where $\frak{k}$ is a compact simple Lie superalgebra and $A$ is a…

We classify the finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras ${\frak{osp}}_{1|2n}$ in terms of the Drinfeld polynomials. The arguments rely on the description of the…

We discuss the category $\cal I$ of level zero integrable representations of loop algebras and their generalizations. The category is not semisimple and so one is interested in its homological properties. We begin by looking at some…

We consider the classification problem for finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras ${\frak{osp}}_{2n|2m}$ with $n\geqslant 2$. We give necessary conditions for an…

In this paper, we introduce a family of indecomposable finite--dimensional graded modules for the current algebra associated to a simple Lie algebra. These modules are indexed by a tuple of partitions one for each positive root of the…

We construct all finite irreducible modules over Lie conformal superalgebras of type W and S.

We find for each simple finitary Lie algebra $\mathfrak{g}$ a category $\mathbb{T}_\mathfrak{g}$ of integrable modules in which the tensor product of copies of the natural and conatural modules are injective. The objects in…

We distinguish a class of irreducible finite representations of conformal Lie (super)algebras. These representations (called universally defined) are the simplest ones from the computational point of view: a universally defined…

In the first part of the paper we give the denominator identity for all simple finite-dimensional Lie super algebras $\frak g\/$ with a non-degenerate invariant bilinear form. We give also a character and (super) dimension formulas for all…