klr algebras
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Author(s):  
Grégoire Naisse ◽  
Pedro Vaz

Abstract We construct a categorification of parabolic Verma modules for symmetrizable Kac–Moody algebras using KLR-like diagrammatic algebras. We show that our construction arises naturally from a dg-enhancement of the cyclotomic quotients of the KLR-algebras. As a consequence, we are able to recover the usual categorification of integrable modules. We also introduce a notion of dg-2-representation for quantum Kac–Moody algebras, and in particular of parabolic 2-Verma modules.


Author(s):  
Doeke Buursma ◽  
Alexander Kleshchev ◽  
David J. Steinberg
Keyword(s):  
Type A ◽  

2020 ◽  
Vol 224 (11) ◽  
pp. 106410 ◽  
Author(s):  
Doeke Buursma ◽  
Alexander Kleshchev ◽  
David J. Steinberg
Keyword(s):  
Type A ◽  

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Henry Kvinge ◽  
Monica Vazirani

International audience We use Khovanov-Lauda-Rouquier (KLR) algebras to categorify a crystal isomorphism between a funda-mental crystal and the tensor product of a Kirillov-Reshetikhin crystal and another fundamental crystal, all in affine type. The nodes of the Kirillov-Reshetikhin crystal correspond to a family of “trivial” modules. The nodes of the fun-damental crystal correspond to simple modules of the corresponding cyclotomic KLR algebra. The crystal operators correspond to socle of restriction and behave compatibly with the rule for tensor product of crystal graphs.


2019 ◽  
Vol 100 (2) ◽  
pp. 447-469
Author(s):  
Peter J. McNamara
Keyword(s):  

2018 ◽  
Vol 12 (8) ◽  
pp. 1887-1921
Author(s):  
Ruslan Maksimau
Keyword(s):  

2018 ◽  
Vol 371 (7) ◽  
pp. 4535-4583 ◽  
Author(s):  
Alexander Kleshchev ◽  
Robert Muth
Keyword(s):  

2018 ◽  
Vol 188 (2) ◽  
pp. 453-512 ◽  
Author(s):  
Anton Evseev ◽  
Alexander Kleshchev

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