Related papers: A categorification of integral Specht modules

Our main goal in this paper is to translate the diagram relating groups, Lie algebras and Hopf algebras to the corresponding 2-objects, i.e. to categorify it. This is done interpreting 2-objects as crossed modules and showing the…

To each graph without loops and multiple edges we assign a family of rings. Categories of projective modules over these rings categorify $U^-_q(\mathfrak{g})$, where $\mathfrak{g}$ is the Kac-Moody Lie algebra associated with the graph.

In this paper, we investigate the supercategories consisting of supermodules over quiver Hecke superalgebras and cyclotomic quiver Hecke superalgebras. We prove that these supercategories provide a supercategorification of a certain family…

In this paper we show that the Rees algebra can be made into a functor on modules over a ring in a way that extends its classical definition for ideals. The Rees algebra of a module M may be computed in terms of a "maximal" map f from M to…

We construct a functor from the Hecke category to a groupoid built from the underlying Coxeter group. This fixes a gap in an earlier work of the authors. This functor provides an abstract realization of the localization of the Hecke…

We describe a number of geometric contexts where categorification appears naturally: coherent sheaves, constructible sheaves and sheaves of modules over quantizations. In each case, we discuss how "index formulas" allow us to easily perform…

Let $F$ be a local field of mixed characteristic, let $k$ be a finite extension of its residue field, let ${\mathcal H}$ be the pro-$p$-Iwahori Hecke $k$-algebra attached to ${\rm GL}_{d+1}(F)$ for some $d\ge1$. We construct an exact and…

We observe that on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of characteristic $p> h$ (where $h$ is the Coxeter number), with a given (generalized) central character are…

We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…

The monoidal category of Soergel bimodules categorifies the Hecke algebra of a finite Weyl group. In the case of the symmetric group, morphisms in this category can be drawn as graphs in the plane. We define a quotient category, also given…

Previously, the last two authors found large families of decomposable Specht modules labelled by bihooks, over the Iwahori--Hecke algebra of type $B$. In most cases we conjectured that these were the only decomposable Specht modules…

We construct graded homomorphisms between Specht modules of quiver Hecke algebras of type A that differ by an ``$e$-small'' partition-shaped removable set of nodes by expanding on methods by Lyle and Mathas. Our main result constitutes a…

Silting modules are abundant. Indeed, they parametrise the definable torsion classes over a noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also the universal localisations of a hereditary ring, or…

In a previous work, we have associated a complete differential graded Lie algebra to any finite simplicial complex in a functorial way. Similarly, we have also a realization functor from the category of complete differential graded Lie…

For an ample groupoid $\mathcal{G}$ and a unit $x$ of $\mathcal{G}$, Steinberg constructed the induction and restriction functors between the category of modules over the Steinberg algebra $A_R(\mathcal{G})$ and the category of modules over…

Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category…

We prove that applying a projective functor to a holonomic simple module over a semi-simple finite dimensional complex Lie algebra produces a module that has an essential semi-simple submodule of finite length. This implies that holonomic…

We study the classification of submodules of module categories over monoidal categories, extending ideas of Coulembier on the classification of tensor ideals in monoidal categories. We develop a framework that applies to module categories…

We study exact module categories over the representation categories of finite-dimensional quasi-Hopf algebras. As a consequence we classify exact module categories over some families of pointed tensor categories with cyclic group of…

Let $\mathcal{C}$ be a small category. We investigate ringed sites $(\mathbf{C},\mathfrak{R})$ on $\mathcal{C}$ and the resulting module categories $\mathfrak{M}{\rm od}\text{-}\mathfrak{R}$. When $\mathcal{C}$ is finite, based on…