Abstract
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We consider an “orientifold” generalization of Khovanov–Lauda–Rouquier algebras,
depending on a quiver with an involution and a framing. Their representation
theory is related, via a Schur–Weyl duality type functor, to Kac–Moody quantum
symmetric pairs, and, via a categorification theorem, to highest weight modules over
an algebra introduced by Enomoto and Kashiwara. Our first main result is a new
shuffle realization of these highest weight modules and a combinatorial construction
of their PBW and canonical bases in terms of Lyndon words. Our second main
result is a classification of irreducible representations of orientifold KLR algebras
and a computation of their global dimension in the case when the framing is
trivial.
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Keywords
Khovanov–Lauda–Rouquier algebra, Enomoto–Kashiwara algebra,
canonical bases, Lyndon words
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Mathematical Subject Classification
Primary: 81R50, 17B37, 20C08, 18N25
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Milestones
Received: 3 May 2022
Revised: 17 October 2022
Accepted: 21 January 2023
Published: 23 May 2023
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| © 2023 The Author(s), under
exclusive license to MSP (Mathematical Sciences Publishers).
Distributed under the Creative Commons
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