Related papers: Trace decategorification of the Hecke category

We define closed model category structures on different categories connected to the world of operad algebras over the category C(k) of (unbounded) complexes of k-modules: on the category of operads, on the category of algebras over a fixed…

We classify the prelocalizing subcategories of the category of quasi-coherent sheaves on a locally noetherian scheme. In order to give the classification, we introduce the notion of a local filter of subobjects of the structure sheaf. The…

We introduce the notion of categorical absorption of singularities: an operation that removes from the derived category of a singular variety a small admissible subcategory responsible for singularity and leaves a smooth and proper…

We study the cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we show that there is a bijection between tagged curves and string objects. Applications include…

We define extension $\infty$-categories for exact $\infty$-categories in terms of bifibrations. Extension $\infty$-categories are invariant when passing to the stable hull, and consequently we show that they form an $\Omega$-spectrum,…

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…

We describe an algorithm for computing the $p$-canonical basis of the Hecke algebra, or one of its antispherical modules. The algorithm does not operate in the Hecke category directly, but rather uses a faithful embedding of the Hecke…

In this article we show how the Dedekind-Hasse criterion may be applied to prove a simple result about quadratic number fields that usually is derived as a consequence of the theory of ideals and ideal classes.

In the setting of homotopy type theory, each type can be interpreted as a space. Moreover, given an element of a type, i.e. a point in the corresponding space, one can define another type which encodes the space of loops based at this…

We introduce the category of finite strings and study its basic properties. The category is closely related to the augmented simplex category, and it models categories of linear representations. Each lattice of non-crossing partitions…

The traces of the Murphy operators of the Hecke algebra $H_n(q)$, and of products of sets of Murphy operators with non-consecutive indices, can be evaluated by a straightforward recursive procedure. These traces are shown to determine all…

We develop category-theoretic framework for universal homogeneous objects, with some applications in the theory of Banach spaces, linear orderings, and in topology of compact spaces.

Let G be a semisimple Lie group and H a uniform lattice in G. The Selberg trace formula is an equality arising from computing in two different ways the traces of convolution operators on the Hilbert space L^2(G/H) associated to test…

We study Hecke algebras of groups acting on trees with respect to geometrically defined subgroups. In particular, we consider Hecke algebras of groups of automorphisms of locally finite trees with respect to vertex and edge stabilizers and…

The present article gives the index formula of the principal congruence subgroups of the Hecke group H_5

The network inference problem consists of reconstructing the edge set of a network given traces representing the chronology of infection times as epidemics spread through the network. This problem is a paradigmatic representative of…

We define tilting subcategories in arbitrary exact categories to archieve the following. Firstly: Unify existing definitions of tilting subcategories to arbitrary exact categories. Discuss standard results for tilting subcategories:…

Coxeter groups are a special class of groups generated by involutions. They play important roles in the various areas of mathematics. This survey particularly focuses on how one uses Coxeter groups to construct interesting examples of…

Under suitably nice conditions, given a coalgebra object in a tensor category we compute the layers of its coradical (socle) filtration.

Let $\mathcal C$ be closed symmetric monoidal Grothendieck category. We define the pure derived category with respect to the monoidal structure via a relative injective model category structure on the category $\mathbf{C}(\mathcal C)$ of…