Year: 2011
Type: article
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].
Source: Compositio Mathematica
Authors: Volodymyr Mazorchuk, Vanessa Miemietz
Institutions: Uppsala University, University of East Anglia
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funders: Vetenskapsrådet, Uppsala Universitet
OpenAlex ID: W2137623472