Representations of cyclotomic oriented Brauer categories

Abstract

The cyclotomic Brauer category OB(u,u′) is an upper finite weakly triangular category over an arbitrary field in the sense of [14, Definition 2.2] and the category of locally finite dimensional representations of A is an upper finite fully stratified category in the sense of [10], where A is the locally unital algebra associated to OB(u,u′). The category of locally finite dimensional representations of A is used to give a direct proof of the tensor product categorification (in the general sense of Losev and Webster) for an integrable lowest weight with an integrable highest weight representation of the same level for the Lie algebra g, where g is a direct sum of copies of sl∞ (resp., slˆp) if the characteristic p of the ground field is 0 (resp., positive). Such a result was expected in [4] when k=C and proved previously in [2] when the level is 1.