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Cell 2-representations of finitary 2-categories
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Geometry and Logic.
2011 (English)In: Compositio Mathematica, ISSN 0010-437X, E-ISSN 1570-5846, Vol. 147, no 5, 1519-1545 p.Article in journal (Refereed) Published
Abstract [en]

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].

Place, publisher, year, edition, pages
2011. Vol. 147, no 5, 1519-1545 p.
Keyword [en]
2-category, cell module, categorification, action, functor, natural transformation, category with full projective functors, finite-dimensional algebra
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-161603DOI: 10.1112/S0010437X11005586ISI: 000296112500009OAI: oai:DiVA.org:uu-161603DiVA: diva2:457755
Available from: 2011-11-19 Created: 2011-11-15 Last updated: 2017-12-08Bibliographically approved

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Mazorchuk, Volodymyr

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