Related papers: Simple transitive $2$-representations of Soergel b…

The theory of representations of a crossed module is a direct generalization of the theory of representations of groups. For a finite group G, the Drinfeld quantum double of the group G is a Hopf algebra that represents a special case of…

This paper generalizes the concepts of 2-local derivations and biderivations (without the skewsymmetric condition) of a finite-dimensional Lie algebra from the adjoint module to any finite-dimensional module, and determines all 2-local…

Soergel bimodules and their Hochschild homology are known to be important in the context of link homology. In this article we observe that Soergel bimodules may be naturally identified as the cohomology of well-defined objects in the…

We describe a new type of $2$-representations, using coherent sheaves. Feigin, Finkelberg, Kuznetsov, Mirkovi\'c and Braverman have provided a construction of Verma modules for complex semi-simple Lie algebras using based quasi-map spaces…

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…

Over an arbitrary field, we prove that the relative 2-Deligne tensor product of two separable module 2-categories over a compact semisimple tensor 2-category exists. This allows us to consider the Morita 4-category of compact semisimple…

We classify Borel-Schur algebras having finite representation type. We also de- termine Auslander-Reiten sequences for a large class of simple modules over Borel- Schur algebras. A partial information on the structure of the socles of…

In this paper, we classify all simple weight modules with finite-dimensional weight spaces over the $N=2$ Ramond algebra. Any such module $V$ is either a simple highest weight module or a simple lowest weight module, or a simple cuspidal…

We classify all simple supermodules over the queer Lie superalgebra $\mathfrak{q}_{2}$ up to classification of equivalence classes of irreducible elements in a certain Euclidean ring.

We study Soergel modules for arbitrary Coxeter groups. For infinite Coxeter groups, we show that the homomorphisms between Soergel modules are in general more than those coming from morphisms of Soergel bimodules. This result provides a…

We examine the partition of a finite Coxeter group of type $B$ into cells determined by a weight function $L$. The main objective of these notes is to reconcile Lusztig's description of constructible representations in this setting with…

We represent a general bilinear Calder\'on-Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so called sparse T1…

We construct a representation of the string 2-group on a 2-vector space, aiming to establish it as the categorification of the spinor representation. Our model for 2-vector spaces is based on the Morita bicategory of von Neumann algebras,…

We show, in full generality, that Lusztig's $\mathbf{a}$-function describes the projective dimension of both indecomposable tilting modules and indecomposable injective modules in the regular block of the BGG category $\mathcal{O}$, proving…

For the cyclic group $C_2$ we give a complete description of the derived category of perfect complexes of modules over the constant Mackey ring $\underline{\mathbb{Z}/\ell}$, for $\ell$ a prime. This is fairly simple for $\ell$ odd, but for…

A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…

We study thick subcategories of the category of 2-term complexes of projective modules over an associative algebra. We show that those thick subcategories that have enough injectives are in explicit bijection with 2-term silting complexes…

Let $W$ be an affine Weyl group, and let $\Bbbk$ be a field of characteristic $p>0$. The diagrammatic Hecke category $\mathcal{D}$ for $W$ over $\Bbbk$ is a categorification of the Hecke algebra for $W$ with rich connections to modular…

In this article we describe the 2-cocycles, Schur multiplier and representation group of discrete Heisenberg groups over the unital rings of order $p^2$. We describe all projective representations of Heisenberg groups with entries from the…

Let $V$ be a simple vertex operator algebra containing a rank $n$ Heisenberg vertex algebra $H$ and let $C=\text{Com}\left( {H}, {V}\right)$ be the coset of ${H}$ in ${V}$. Assuming that the representation categories of interest are vertex…