Related papers: Simple sl_{n+1}-module structures on U(h)

We start the general structure theory of not necessarily semisimple finite tensor categories, generalizing the results in the semisimple case (i.e. for fusion categories), obtained recently in our joint work with D.Nikshych. In particular,…

We investigate several categories of integrable $sl(\infty)$-, $o(\infty)$-, $sp(\infty)$-modules. In particular, we prove that the category of integrable $sl(\infty)$-, $o(\infty)$-, $sp(\infty)$-modules with finite-dimensional weight…

In this paper we study the subcategory of cuspidal modules of the category of weight modules over the Lie algebra sl(n+1). Our main result is a complete classification and explicit description of the indecomposable cuspidal modules.

This paper studies modular forms of rank four and level one. There are two possiblities for the isomorphism type of the space of modular forms that can arise from an irreducible representation of the modular group of rank four, and we…

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a…

Let $\g$ be an arbitrary Kac-Moody algebra with a Cartan sualgebra $\h$. In this paper, we determine the category of $\g$-modules that are free $U(\h)$-modules of rank 1.

In this paper, we construct a novel class of simple modules for the $W$-algebra $W(2,2)$. Our approach involves taking tensor products of finitely many non-weight simple modules $\Omega(\lambda,\alpha,h)$ with an arbitrary simple restricted…

For any $\mathbf{a}=(a_1,\dots,a_n)\in \mathbb{C}^n$, we introduce a Whittaker category $\mathcal{H}_{\mathbf{a}}$ whose objects are $\mathfrak{sl}_{n+1}$-modules $M$ such that $e_{0i}-a_i$ acts locally nilpotently on $M$ for all $i \in…

The purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie…

In this paper, a family of non-weight modules over Lie superalgebras $S(q)$ of Block type are studied. Free $U(\eta)$-modules of rank $1$ over Ramond-Block algebras and free $U(\mathfrak{h})$-modules of rank $2$ over Neveu-Schwarz-Block…

In this paper, the module-algebra structures of $U_q(sl(m+1))$ on the quantum $n$-space $A_q(n)$ are studied. We characterize all module-algebra structures of $U_q(sl(m+1))$ on $A_q(2)$ and $A_q(3)$ when $m\geq 2$. The module-algebra…

We classify all simple $W_n$-modules with finite-dimensional weight spaces. Every such module is either of a highest weight type or is a quotient of a module of tensor fields on a torus, which was conjectured by Eswara Rao. This generalizes…

A subunit in a monoidal category is a subobject of the monoidal unit for which a canonical morphism is invertible. They correspond to open subsets of a base topological space in categories such as those of sheaves or Hilbert modules. We…

This paper is about skew monoidal tensored V-categories (= skew monoidal hommed V-actegories) and their categories of modules. A module over <M,*,R> is an algebra for the monad T = R * _ on M. We study in detail the skew monoidal structure…

Let $R$ be an associative ring with identity. This paper investigates the structure of the monomorphism category of large $R$-modules and establishes connections with the category of contravariant functors defined on finitely presented…

In this paper we classify all the cyclic finite dimensional indecomposable\\ modules of the perfect Lie algebras $\mathfrak{sl}(n+1)\ltimes \mathbbm{C}^{n+1}$, given by the semidirect sum of the simple Lie algebra $A_n$ with its standard…

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…

We generalize the construction of tensor categories of endomorphisms of a type III factor $M$ associated with a $G$-kernel, from the case of a discrete group $G$ to that of a compact second countable group. Our approach is based on the…

Recollements of derived module categories are investigated, using a new technique, ladders of recollements, which are mutation sequences. The position in the ladder is shown to control whether a recollement restricts from unbounded to…

We classify ribbon semisimple monoidal categories with three isomorphism classes of simple objects over the field of complex numbers.