2010/11/15 by Volodymyr Mazorchuk, Vanessa Miemietz · 1 citation
Mathematics · #math.RT
paper · pdf · doi:10.1112/s0010437x11005586
published as Compositio Math. 147 (2011) 1519-1545 · 25 pages
arxiv created 2010/11/15 · arxiv updated 2019/02/20
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 describe in detail (right) cell 2-representations inspired by Kazhdan-Lusztig cell modules for Hecke algebras. Under some natural assumptions we show that cell 2-representations are strongly simple and do not depend on the choice of a right cell inside a two-sided cell. This reproves and extends the uniqueness result on categorification of Kazhdan-Lusztig cell modules for Hecke algebras of type A from \citeMS2.