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Categorified quantum sl2 is an inverse limit of flag 2-categories


Beliakova, Anna; Lauda, Aaron D (2014). Categorified quantum sl2 is an inverse limit of flag 2-categories. Transformation Groups, 19(1):1-26.

Abstract

We prove that categorified quantum sl2 is an inverse limit of Flag 2-categories defined using cohomology rings of iterated flag varieties. This inverse limit is an instance of a 2-limit in a bicategory giving rise to a universal property that characterizes the categorification of quantum sl2 uniquely up to equivalence. As an application we characterize all bimodule homomorphisms in the Flag 2-category and prove that on the homological level the categorified quantum Casimir of sl2 acts appropriately on these 2-representations.

Abstract

We prove that categorified quantum sl2 is an inverse limit of Flag 2-categories defined using cohomology rings of iterated flag varieties. This inverse limit is an instance of a 2-limit in a bicategory giving rise to a universal property that characterizes the categorification of quantum sl2 uniquely up to equivalence. As an application we characterize all bimodule homomorphisms in the Flag 2-category and prove that on the homological level the categorified quantum Casimir of sl2 acts appropriately on these 2-representations.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:15 February 2014
Deposited On:30 Sep 2014 14:03
Last Modified:08 Dec 2017 07:16
Publisher:Springer
ISSN:1083-4362
Publisher DOI:https://doi.org/10.1007/s00031-014-9250-4

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