Related papers: On a category of $gl_{\infty}$-modules

In Finite Group Modular Representation Theory, the basic objects are the indecomposable and simple modules. This paper offers a new classification of these objects that refines the Green Theory Classification of indecomposable and simple…

Modular Tensor Categories (MTC's) arise in the study of certain condensed matter systems. There is an ongoing program to classify MTC's of low rank, up to modular data. We present an overview of the methods to classify modular tensor…

We prove that if C is a tensor C*-category in a certain class, then there exists an uncountable family of pairwise non stably isomorphic II_1 factors (M_i) such that the bimodule category of M_i is equivalent to C for all i. In particular,…

We define a filtration indexed by the integers on the tensor product of an integrable highest weight module and a loop module for a quantum affine algebra. We prove that the filtration is either trivial or strictly decreasing and give…

We study strongly graded vertex algebras and their strongly graded modules, which are conformal vertex algebras and their modules with a second, compatible grading by an abelian group satisfying certain grading restriction conditions. We…

We categorify Verma and indecomposable projective modules in the category $\mathcal I_{\mathfrak{g}}(\mathfrak{sl}_2)$ for $\mathfrak{sl}_2$ using a tensor product decomposition theorem of T. J. Enright and work of J. Chuang and R.…

In this paper, by using functor rings and functor categories, we study finiteness and purity of subcategories of the module categories. We give a characterisation of contravariantly finite resolving subcategories of the module category of…

We consider the category of Harish-Chandra modules for ${\rm SL}_2(\mathbb R)$ as a module over the category of finite-dimensional representations of ${\rm SL}(2)$ with respect to the tensor product. In this note we use classical results…

We prove that the tensor product of a simple and a finite dimensional $\mathfrak{sl}_n$-module has finite type socle. This is applied to reduce classification of simple $\mathfrak{q}(n)$-supermodules to that of simple…

For a finite tensor category $\mathcal C$ and a Hopf monad $T:\mathcal C\to \mathcal C$ satisfying certain conditions we describe exact indecomposable left $\mathcal C^T$-module categories in terms of left $\mathcal C$-module categories and…

We construct a dg-enhancement of KLRW algebras that categorifies the tensor product of a universal $\mathfrak{sl}_2$ Verma module and several integrable irreducible modules. When the integrable modules are two-dimensional, we construct a…

We classify all irreducible generic $\mathrm{VI}$-modules in non-describing characteristic. Our result degenerates to yield a classification of irreducible generic $\mathrm{FI}$-modules in arbitrary characteristic. Our result can also be…

In this paper we study Category $\mcal O$ for the polynomial toroidal Lie algebras and its $S,H$ type subalgebras. We classify irreducible objects of category $\mcal O$ as unique irreducble quotient of standard modules. Surprisingly,…

We develop a categorical analogue of Clifford theory for strongly graded rings over graded fusion categories. We describe module categories over a fusion category graded by a group $G$ as induced from module categories over fusion…

Working over an arbitrary field, we define compact semisimple 2-categories, and show that every compact semisimple 2-category is equivalent to the 2-category of separable module 1-categories over a finite semisimple tensor 1-category. Then,…

We study Karoubian tensor categories which interpolate representation categories of families of so-called easy quantum groups in the same sense in which Deligne's interpolation categories $\mathrm{\underline{Rep}}(S_t)$ interpolate the…

In this paper, we use basic formal variable techniques to study certain categories of modules for the toroidal Lie algebra $\tau$. More specifically, we define and study two categories $\mathcal{E}_{\tau}$ and $\mathcal{C}_{\tau}$ of…

We give a necessary and sufficient condition in terms of group cohomology for two indecomposable module categories over a group-theoretical fusion category ${\mathcal C}$ to be equivalent. This concludes the classification of such module…

Let $k$ be an algebraically closed field of characteristic $0$ or $p>2$. Let $\mathcal{G}$ be an affine supergroup scheme over $k$. We classify the indecomposable exact module categories over the tensor category ${\rm sCoh}_{\rm…

We classify integrable bounded simple weight modules over classical Lie superalgebras at infinity. We also study the categories of such modules, and we prove that for most of the classical Lie superalgebras at infinity the respective…