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

Various definitions of chiral observables in a given Moebius covariant two-dimensional theory are shown to be equivalent. Their representation theory in the vacuum Hilbert space of the 2D theory is studied. It shares the general…

We study a 2-functor that assigns to a bimodule category over a finite k-linear tensor category a k-linear abelian category. This 2-functor can be regarded as a category-valued trace for 1-morphisms in the tricategory of finite tensor…

We characterize in terms of bicategories actions of monoidal categories to representation categories of algebras. For that purpose we introduce cocycles in any 2-category $\K$ and the category of Tambara modules over a monad $B$ in $\K$. We…

The notion of permutative representation is generalized to the $2$-adic ring $C^*$-algebra $\mathcal{Q}_{2}$. Permutative representations of $\mathcal{Q}_2$ are then investigated with a particular focus on the inclusion of the Cuntz algebra…

We study irreducible representations of two classes of conformal Galilei algebras in 1-spatial dimension. We construct a functor which transforms simple modules with nonzero central charge over the Heisenberg subalgebra into simple modules…

We realize the Temperley-Lieb algebra by analogues of Soergel bimodules. The key point is that the monoidal structure is not given by a usual tensor product but by a slightly more complicated operation.

We determine the dual modules of all irreducible modules of alternating groups over fields of characteristic 2.

We investigate explicit modular forms of weights $1/2$ and $3/2$-classical, minus, and fermionic theta series-arising from the classical Weil representation associated to $\operatorname{SL}_2(\mathbb{R})$ via the $2$-cocycles of Rao, Kudla,…

Let k be a field. A finite dimensional k-algebra is said to be minimal representation-infinite provided it is representation-infinite and all its proper factor algebras are representation-finite. Our aim is to classify the special biserial…

For an arbitrary commutative ring k and t in k, we construct a 2-functor S_t which sends a tensor category to a new tensor category. By applying it to the representation category of a bialgebra we obtain a family of categories which…

For an affine algebraic variety $X$ we study a category of modules that admit compatible actions of both the algebra of functions on $X$ and the Lie algebra of vector fields on $X$. In particular, for the case when $X$ is the sphere…

We discuss the category $\cal I$ of level zero integrable representations of loop algebras and their generalizations. The category is not semisimple and so one is interested in its homological properties. We begin by looking at some…

Polynomial representations of general linear groups and modules over Schur algebras are compared. We work over an arbitrary commutative ring and show that Schur-Weyl duality is the key for an equivalence between both categories.

We prove the relative hard Lefschetz theorem for Soergel bimodules. It follows that the structure constants of the Kazhdan-Lusztig basis are unimodal. We explain why the relative hard Lefschetz theorem implies that the tensor category…

We define A-infinity-bimodules similarly to Tradler and show that this notion is equivalent to an A-infinity-functor with two arguments which takes values in the differential graded category of complexes of k-modules, where k is a ground…

In this paper we develop representation theory of the two fold central extension of SL(2) over the field of 2-adic numbers. As a consequence, we obtain a local Shimura correspondence between the two fold central extension of SL(2) and the…

A Chevalley type integral basis for the ortho-symplectic Lie superalgebra is constructed. The simple modules of the ortho-symplectic supergroup over an algebraically closed field of prime characteristic not equal to 2 are classified, where…

We prove a tensor equivalence between full subcategories of a) graded matrix factorisations of the potential x^d-y^d and b) representations of the N=2 minimal super vertex operator algebra at central charge 3-6/d, where d is odd. The…

We construct all finite irreducible modules over Lie conformal superalgebras of type W and S.

We show that the space of invariants for the Weil representation for discriminant groups which contain self-dual isotropic subgroups is spanned by the characteristic functions of the self-dual isotropic subgroups. As an application, we…