Parabolic projective functors in type A

Abstract

Abstract. We classify projective functors on the regular block of RochaCaridi's parabolic version of the BGG category O in type A. In fact, we show that, in type A, the restriction of an indecomposable projective functor from O to the parabolic category is either indecomposable or zero. As a consequence, we obtain that projective functors on the parabolic category O in type A are completely determined, up to isomorphism, by the linear transformations they induce on the level of the Grothendieck group, which was conjectured by Stroppel in [St3].

Simple transitive 2-representations for some 2-subcategories of Soergel bimodules

“…This is extended in [MM6] to more general 2-categories and (slightly) more general classes of 2representations. Some nice applications of these classification results were obtained in [KM1].…”

Classification problems in 2-representation theory

“…In [30], classification of simple transitive 2-representation for the 2-category of Soergel bimodules in type A (cf. Theorem 11) was used to classify indecomposable projective functors on the principal block of BGG category O for sl n .…”

Characterisation and applications of $\Bbbk$-split bimodules

“…The importance of this problem is supported by interesting applications, see e.g. [KiM1]. The case of the algebra A treated in this paper differs significantly from all previously studied cases.…”