Cell 2-representations of finitary 2-categories

By Volodymyr Mazorchuk, Vanessa Miemietz. Compositio Mathematica, 2010

106 citations recorded by the source corpus.

Abstract 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 [V. Mazorchuk and C. Stroppel, Categorification of (induced) cell modules and the rough structure of generalised Verma modules, Adv. Math. 219 (2008), 1363–1426].

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b632aa8b516d880ce90a9b7433e26c69e5e2f38b

Citations in the corpus

• Endomorphisms of cell 2-representations (2012, unknown): “A 2-category C is called finitary (over k), see [11], if the following conditions are satisfied:”