Related papers: On near-group centers and super-modular categories
In his theory of unipotent characters of finite groups of Lie type, Lusztig constructed modular categories from two-sided cells in Weyl groups. Brou\'e,Malle and Michel have extended parts of Lusztig's theory to complex reflection groups.…
The definitions of the $n^{th}$ Gauss sum and the associated $n^{th}$ central charge are introduced for premodular categories $\mathcal{C}$ and $n\in\mathbb{Z}$. We first derive an expression of the $n^{th}$ Gauss sum of a modular category…
We study the structure of the vector space of Drinfeld quasi-modular forms for congruence subgroups. We provide representations as polynomials in the false Eisenstein series with coefficients in the space of Drinfeld modular forms (the…
Although it has been a well-known fact, for more than two decades, that category theory is needed for the study of topological orders, it is still a non-trivial challenge for students and working physicists to master the abstract language…
By using the approach in \cite{XX2006} to Hall algebras arising in homologically finite triangulated categories, we find an `almost' associative multiplication structure for indecomposable objects in a 2-periodic triangulated category. As…
In this paper we study categories of tilting modules. Our starting point is the tilting modules for a reductive algebraic group G in positive characteristic. Here we extend the main result in [8] by proving that these tilting modules form a…
When travelling from the number fields theory to the function fields theory, one cannot miss the deep analogy between rank 1 Drinfeld modules and the group of root of unity and the analogy between rank 2 Drinfeld modules and elliptic…
In Rev. Math. Phys. 4 (1997) 785 we study Hilbert-C* systems {F,G} where the fixed point algebra A has nontrivial center Z and where A'\cap F=Z is satisfied. The corresponding category of all canonical endomorphisms of A contains…
Let $A$ be an algebra over a commutative ring $k$. We compute the center of the category of $A$-bimodules. There are six isomorphic descriptions: the center equals the weak center, and can be described as categories of noncommutative…
We prove that for a large class of well-behaved cocomplete categories $\mathcal C$ the weak and strong Drinfeld centers of the monoidal category $\mathcal{E}$ of cocontinuous endofunctors of $\mathcal{C}$ coincide. This generalizes similar…
In this paper we generalise the notion of Drinfeld modular form for the group $\Gamma$ := GL2(Fq[$\theta$]) to a vector-valued setting, where the target spaces are certain modules over positive characteristic Banach algebras over which are…
We advance the classification of fusion categories in two directions. Firstly, we completely classify integral fusion categories -- and consequently, semi-simple Hopf algebras -- of dimension $pq^2$, where $p$ and $q$ are distinct primes.…
Let $k$ be a commutative $\mathbb{Q}$-algebra. We study families of functors between categories of finitely generated $R$-modules which are defined for all commutative $k$-algebras $R$ simultaneously and are compatible with base changes.…
Modular categories are a well-known source of quantum 3-manifold invariants. In this paper we study structures on modular categories which allow to define refinements of quantum 3-manifold invariants involving cohomology classes or…
We construct the first examples of purely continuous, $q$-deformed Lie type locally compact quantum groups in higher rank. They arise from Drinfeld-Jimbo quantization, at unimodular deformation parameter, of the totally positive part of…
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…
This paper contains the written notes of a course the author gave at the VIASM of Hanoi in the Summer 2018. It provides an elementary introduction to the analytic naive theory of Drinfeld modular forms for the simplest 'Drinfeld modular…
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 introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer…
In this paper, we try to answer the following question: given a modular tensor category $\A$ with an action of a compact group $G$, is it possible to describe in a suitable sense the ``quotient'' category $\A/G$? We give a full answer in…