Cell 2-representations of finitary 2-categories

Mazorchuk, Volodymyr and Miemietz, Vanessa (2011) Cell 2-representations of finitary 2-categories. Compositio Mathematica, 147 (05). pp. 1519-1545. ISSN 0010-437X

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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].

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Depositing User:	Users 2731 not found.
Date Deposited:	29 Nov 2011 10:04
Last Modified:	07 Nov 2024 12:32
URI:	https://ueaeprints.uea.ac.uk/id/eprint/35568
DOI:	10.1112/S0010437X11005586

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