Vanessa Miemietz

Cell 2-representations of finitary 2-categories

We study 2-representations of finitary 2-categories with involution and adjunctions by functors on module categories over finite-dimensional algebras. In particular, we define, construct and descri ...

Morita theory for finitary 2-categories

We develop Morita theory for finitary additive 2-representations of finitary 2-categories. As an application we describe Morita equivalence classes for 2-categories of projective functors associated to finite dimensional algebras and for 2-categories of Soergel bimodules.

Isotypic faithful 2-representations of {\mathcal {J}}-simple fiat 2-categories

We introduce the class of isotypic 2-representations for finitary 2-categories and the notion of inflation of 2-representations. Under some natural assumptions we show that isotypic 2-representations are equivalent to inflations of cell 2-representations.

RATIONAL REPRESENTATIONS OF GL 2

Let F be an algebraically closed field of characteristic p . We fashion an infinite dimensional basic algebra ← p ( F ), with a transparent combinatorial structure, which controls the rational representation theory of GL 2 ( F ).

Homotopy, homology, and GL2

We define weak 2-categories of finite dimensional algebras with bimodules, along with collections of operators

Endomorphisms of Cell 2-Representations

\mathbb{O}_{(c,x)}

Additive Versus Abelian 2-Representations of Fiat 2-Categories

on these 2-categories. We prove that special examples

Transitive 2-representations of finitary 2-categories

\mathbb{O}_p

Serre functors for Lie algebras and superalgebras

of these operators control all homological aspects of the rational representation theory of the algebraic group

Affine cellularity of affine Hecke algebras of rank two

GL_2