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

We prove a uniqueness theorem for irreducible non-critical Gelfand-Tsetlin modules. The uniqueness result leads to a complete classification of the irreducible Gelfand-Tsetlin modules with 1-singularity. An explicit construction of such…

We study the category M consisting of U(sl_{n+1})-modules whose restriction to U(h) is free of rank 1, in particular we classify isomorphism classes of objects in M and determine their submodule structure. This leads to new…

We give an elementary construction of a $p\geq 1$-singular Gelfand-Tsetlin $\mathfrak{gl}_n(\mathbb C)$-module in terms of local distributions. This is a generalization of the universal $1$-singular Gelfand-Tsetlin $\mathfrak{gl}_n(\mathbb…

For a finite group scheme G over an algebraically closed field k of characteristic p>0 we study G-modules M, which are defined in terms of properties of their pull-backs along p-points of G. We show that the corresponding subcategories…

We study a class of representations over the degenerate double affine Hecke algebra of gl_n by an algebraic method. As fundamental objects in this class, we introduce certain induced modules and study some of their properties. In…

We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…

We study (relative) $\mathcal K$-Mittag-Leffler modules as was done in the author's habilitation thesis, rephrase old, unpublished results in terms of definable subcategories, and present newer ones, culminating in a characterization of…

We identify the type of $\mathbb{C}[[\hbar]]$-linear structure inherent in the $\infty$-categories which arise in the theory of Deformation Quantization modules. Using this structure, we show that the $\infty$-category of quasicoherent…

In this article we give application of closure operators in category of modules. Our main result shows that every subcategory A of injective modules of R-mod (under a mild condition) induces a torsion theory of R-mod.

We classify the localizing tensor ideals of the integral stable module category for any finite group $G$. This results in a generic classification of $\mathbb{Z}[G]$-lattices of finite and infinite rank and globalizes the modular case…

We investigate infinite dimensional modules for a linear algebraic group $\mathbb G$ over a field of positive characteristic $p$. For any subcoalgebra $C \subset \mathcal O(\mathbb G)$ of the coordinate algebra of $\mathbb G$, we consider…

We introduce a semisimple tensor category $\mc{O}^{int}_q(m|n)$ of modules over an quantum ortho-symplectic superalgebra. It is a natural counterpart of the category of finitely dominated integrable modules over the quantum classical…

In this paper we explore the possibility of endowing simple infinite-dimensional ${\mathfrak{sl}_2(\mathbb{C})}$-modules by the structure of the graded module. The gradings on finite-dimensional simple module over simple Lie algebras has…

We show that if $V$ is a vertex operator algebra such that all the irreducible ordinary $V$-modules are $C_1$-cofinite and all the grading-restricted generalized Verma modules for $V$ are of finite length, then the category of finite length…

The tensor ideal localising subcategories of the stable module category of all, including infinite dimensional, representations of a finite group scheme over a field of positive characteristic are classified. Various applications concerning…

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…

For an untwisted affine Lie algebra we prove an embedding of any higher level Demazure module into a tensor product of lower level Demazure modules (e.g. level one in type A) which becomes in the limit (for anti-dominant weights) the…

In this article, we study the classification of some natural numbers related to the combinatorics of congruence subgroups of the modular group. More precisely, we will focus here on the notion of minimal monomial solutions. These are the…

We define fully exact module categories, a subclass of exact module categories over a finite braided tensor category that is stable under the relative Deligne product. In contrast, we demonstrate with examples in both zero and non-zero…

Let $R$ be a Noetherian ring and let $C$ be a semidualizing $R$-module. In this paper, we are concerned with the tensor and torsion product of $C$-injective modules. Firstly, it is shown that the tensor product of any two $C$-injective…