60 citations · 225 across the 37 of their papers we have counts for
41 papers · 1 filter
Categorification in Representation Theory
Vanessa Miemietz
In this survey article, we give an introduction to the relatively young subject of -representation theory, which studies categorifications of important players in classical repr…
The subregular and submaximal -cells
Vanessa Miemietz, Marie Roth, Daniel Tubbenhauer
Cells for the canonical and -canonical bases organise the representation theory and geometry of Hecke categories. We determine the relevant -canonical basis elements and the…
Almost finitary birepresentation theory and applications to affine Soergel bimodules
Marco Mackaay, Vanessa Miemietz, Pedro Vaz
In this article, we develop a generalization of finitary birepresentation theory applicable to Soergel bimodules for infinite Coxeter groups. We establish a reduction process for t…
Induction for extended affine type A Soergel bimodules: first steps
Marco Mackaay, Vanessa Miemietz, Pedro Vaz
In this paper we take the first steps towards the categorification of the Zelevinsky tensor product of finite dimensional representations of extended affine type A Hecke algebras.
Hochschild cohomology for finitary 2-representations
James Macpherson, Vanessa Miemietz, Mateusz Stroiński
In this article, we define and investigate Hochschild cohomology for finitary 2-representations of quasi-fiat 2-categories.
Applying projective functors to arbitrary holonomic simple modules
Marco Mackaay, Volodymyr Mazorchuk, Vanessa Miemietz
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-simp…
Differential graded cell 2-representations
Robert Laugwitz, Vanessa Miemietz
This article develops a theory of cell combinatorics and cell 2-representations for differential graded 2-categories. We introduce two types of partial preorders, called the strong…
Basic Hopf algebras and symmetric bimodules
Katerina Hristova, Vanessa Miemietz
Motivated by the so-called H-cell reduction theorems, we investigate certain classes of bicategories which have only one H-cell apart from possibly the identity. We show that H_0-s…
Evaluation birepresentations of affine type A Soergel bimodules
M. Mackaay, V. Miemietz, P. Vaz
In this paper, we use Soergel calculus to define a monoidal functor, called the evaluation functor, from extended affine type A Soergel bimodules to the homotopy category of bounde…
Pretriangulated 2-representations via dg algebra 1-morphisms
Robert Laugwitz, Vanessa Miemietz
This paper develops a theory of pretriangulated 2-representations of dg 2-categories. We characterize cyclic pretriangulated 2-representations, under certain compactness assumption…
Kostant's problem for fully commutative permutations
Marco Mackaay, Volodymyr Mazorchuk, Vanessa Miemietz
We give a complete combinatorial answer to Kostant's problem for simple highest weight modules indexed by fully commutative permutations. We also propose a reformulation of Kostant…
The -Stable Category
Jeremy R. B. Brightbill, Vanessa Miemietz
A well-known theorem of Buchweitz provides equivalences between three categories: the stable category of Gorenstein projective modules over a Gorenstein algebra, the homotopy categ…
Uniqueness of exact Borel subalgebras and bocses
Julian Külshammer, Vanessa Miemietz
Together with Koenig and Ovsienko, the first author showed that every quasi-hereditary algebra can be obtained as the (left or right) dual of a directed bocs. In this monograph, we…
Finitary birepresentations of finitary bicategories
Marco Mackaay, Volodymyr Mazorchuk, Vanessa Miemietz +2
In this paper, we discuss the generalization of finitary -representation theory of finitary -categories to finitary birepresentation theory of finitary bicategories. In previ…
Simple transitive -representations of Soergel bimodules for finite Coxeter types
Marco Mackaay, Volodymyr Mazorchuk, Vanessa Miemietz +2
In this paper we show that Soergel bimodules for finite Coxeter types have only finitely many equivalence classes of simple transitive -representations and we complete their cla…
2-categories of symmetric bimodules and their 2-representations
Volodymyr Mazorchuk, Vanessa Miemietz, Xiaoting Zhang
In this article we analyze the structure of -categories of symmetric projective bimodules over a finite dimensional algebra with respect to the action of a finite abelian group.…
Coidempotent subcoalgebras and short exact sequences of finitary 2-representations
Aaron Chan, Vanessa Miemietz
In this article, we study short exact sequences of finitary 2-representations of a weakly fiat 2-category. We provide a correspondence between such short exact sequences with fixed…
Trihedral Soergel bimodules
Marco Mackaay, Volodymyr Mazorchuk, Vanessa Miemietz +1
The quantum Satake correspondence relates dihedral Soergel bimodules to the semisimple quotient of the quantum representation category. It also establishes a prec…
Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations
Marco Mackaay, Volodymyr Mazorchuk, Vanessa Miemietz +1
The main result of this paper establishes a bijection between the set of equivalence classes of simple transitive -representations with a fixed apex of a fiat -…
Cell 2-Representations and Categorification at Prime Roots of Unity
Robert Laugwitz, Vanessa Miemietz
Motivated by recent advances in the categorification of quantum groups at prime roots of unity, we develop a theory of 2-representations for 2-categories enriched with a p-differen…
Pyramids and 2-representations
Volodymyr Mazorchuk, Vanessa Miemietz, Xiaoting Zhang
We describe a diagrammatic procedure which lifts strict monoidal actions from additive categories to categories of complexes avoiding any use of direct sums. As an application, we…
Characterisation and applications of -split bimodules
Volodymyr Mazorchuk, Vanessa Miemietz, Xiaoting Zhang
We describe the structure of bimodules (over finite dimensional algebras) which have the property that the functor of tensoring with such a bimodule sends any module to a projectiv…
Simple transitive 2-representations via (co)algebra 1-morphisms
Marco Mackaay, Volodymyr Mazorchuk, Vanessa Miemietz +1
For any fiat 2-category C, we show how its simple transitive 2-representations can be constructed using coalgebra 1-morphisms in the injective abelianization of C. Dually, we show…
Affine quiver Schur algebras and -adic
Vanessa Miemietz, Catharina Stroppel
In this paper we consider the (affine) Schur algebra introduced by Vignéras as the endomorphism algebra of certain permutation modules for the Iwahori-Matsumoto Hecke algebra. This…