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- Title
Cell 2-representations of finitary 2-categories.
- Authors
Mazorchuk, Volodymyr; Miemietz, Vanessa
- 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].
- Subjects
REPRESENTATIONS of algebras; CATEGORIES (Mathematics); FUNCTOR theory; VERMA modules; HECKE algebras; MODULES (Algebra); DIMENSION theory (Algebra); KAZHDAN-Lusztig polynomials
- Publication
Compositio Mathematica, 2011, Vol 147, Issue 5, p1519
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X11005586