Related papers: Quantum loop modules

For each integer $t>0$ and each complex simple Lie algebra $\mathfrak{g}$, we determine the least dimension of an irreducible highest weight representation of $\mathfrak{g}$ whose highest weight has height $t$. As a corollary, we classify…

In this article we initiate a systematic study of irreducible weight modules over direct limits of reductive Lie algebras, and in particular over the simple Lie algebras $A(\infty)$, $B(\infty)$, $C(\infty)$ and $D(\infty)$. Our main tool…

We classify the irreducible finite-dimensional representations of the twisted quantum affine algebras.

Over the past three decades, there have been several attempts to characterize modules over affine Lie superalgebras. One of the main issues in this regard is dealing with zero-level modules. In this paper, we study these modules and…

We give a general way of representing the crystal (base) corresponding to the intgrable highest weight modules of quantum Kac-Moody algebras, which is called polyhedral realizations. This is applied to describe explicitly the crystal bases…

Since 2020, finite weight modules have been studied over twisted affine Lie superalgebras. To complete the characterization of modules over affine Lie superalgebras, we need some information regarding modules over untwisted affine Lie…

This paper studies classical weight modules over the $\imath$quantum group $\mathbf{U}^{\imath}$ of type AI. We introduce the notion of based $\mathbf{U}^{\imath}$-modules by generalizing the notion of based modules over the quantum groups.…

We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module…

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…

In this paper, we study a class of non-weight modules over two kinds of algebras related to the Virasoro algebra, i.e., the loop-Virasoro algebras $\mathfrak{L}$ and a class of Block type Lie algebras $\mathfrak{B(q)}$, where $q$ is a…

Finite W-algebras are certain associative algebras arising in Lie theory. Each W-algebra is constructed from a pair of a semisimple Lie algebra g (our base field is algebraically closed and of characteristic 0) and its nilpotent element e.…

For any finitely generated abelian group $Q$, we reduce the problem of classification of $Q$-graded simple Lie algebras over an algebraically closed field of "good" characteristic to the problem of classification of gradings on simple Lie…

We will classify finite dimensional irreducible modules for affine quantum Schur algebras at roots of unity and generalize \cite[(6.5f) and (6.5g)]{Gr80} to the affine case in this paper.

We study the universal integrable modules W_q(m) of level zero for quantum affine sl_2 and a family of maximal finite--dimensional quotients of these modules. We show that these all have dimension 2^m. Using this, we are able to realize…

Block type Lie algebras have been studied by many authors in the latest twenty years. In this paper, we will study a class of more general Block type Lie algebra $\mathcal{B}(p,q)$, which is a class of infinite-dimensional Lie algebra by…

We describe the category of integrable sl(1|n)^ -modules with the positive central charge and show that the irreducible modules provide the full set of irreducible representations for the corresponding simple vertex algebra.

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,…

For a nondegenerate additive subgroup $G$ of the $n$-dimensional vector space $F^n$ over an algebraically closed field $F$ of characteristic zero, there is an associative algebra and a Lie algebra of Weyl type $W(G,n)$ spanned by all…

We study the category of graded finite-dimensional representations of the polynomial current algebra associated to a simple Lie algebra. We prove that the category has enough injectives and compute the graded character of the injective…

We give closed formulae for the q-characters of the fundamental representations of the quantum loop algebra of a classical Lie algebra in terms of a family of partitions satisfying some simple properties. We also give the multiplicities of…