Bases for local Weyl modules for the hyper and truncated current sl(2)-algebras

Bases for local Weyl modules for the hyper and truncated current sl(2)-algebras

Author Bianchi, Angelo Autor UNIFESP Google Scholar
Wilson, Evan Google Scholar
Abstract We use the theory of Grobner-Shirshov bases for ideals to construct linear bases for graded local Weyl modules for the (hyper) current and the truncated current algebras associated to the finite-dimensional complex simple Lie algebra sl(2). The main result is a characteristic-free construction of bases for this important family of modules for the hyper current sl(2)-algebra. In the positive characteristic setting this work represents the first construction in the literature. In the characteristic zero setting, the method provides a different construction of the Chari-Pressley (also Kus-Littelmann) bases and the Chari-Venkatesh bases for local Weyl modules for the current sl(2)-algebra. Our construction allows us to obtain new bases for the local Weyl modules for truncated current sl(2)-algebras with very particular properties. (C) 2018 Elsevier Inc. All rights reserved.
Keywords Grobner-Shirshov bases
Hyper current algebra
Local Weyl modules
Language English
Sponsor CNPq
Grant number CNPq: 462315/2014-2
FAPESP: 2015/22040-0
FAPESP: 2014/09310-5
FAPESP: 2011/12079-5
Date 2018
Published in Journal Of Algebra. San Diego, v. 506, p. 509-539, 2018.
ISSN 0021-8693 (Sherpa/Romeo, impact factor)
Publisher Academic Press Inc Elsevier Science
Extent 509-539
Access rights Closed access
Type Article
Web of Science ID WOS:000433270600021

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