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 describeâ€¦ (More)

We study connections between additive and abelian 2-representations of fiat 2-categories, describe combinatorics of 2-categories in terms of multisemigroups and determine the annihilator of a cellâ€¦ (More)

We introduce the class of isotypic 2-representations for finitary 2categories and the notion of inflation of 2-representations. Under some natural assumptions we show that isotypic 2-representationsâ€¦ (More)

In this article, we define and study the class of simple transitive 2-representations of finitary 2-categories. We prove a weak version of the classical Jordan-HÃ¶lder Theorem where the weakâ€¦ (More)

We determine the endomorphism categories of cell 2-representations of fiat 2-categories associated with strongly regular two-sided cells under some natural assumptions. Along the way, we completelyâ€¦ (More)

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 associatedâ€¦ (More)

We propose a new realization, using Harish-Chandra bimodules, of the Serre functor for the BGG category O associated to a semi-simple complex finite dimensional Lie algebra. We further show that ourâ€¦ (More)

The Lascoux-Leclerc-Thibon-Ariki theory asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotentâ€¦ (More)

Arikiâ€™s and Grojnowskiâ€™s approach to the representation theory of affine Hecke algebras of type A is applied to type B with unequal parameters to obtain â€“ under certain restrictions on theâ€¦ (More)