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

Autor(es)

Bianchi, Angelo ^[1] ; Wilson, Evan ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Paulo, UNIFESP, Dept Sci & Technol, Sao Paulo - Brazil

^[2] Penn State Brandywine, Media, PA - USA

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 506, p. 509-539, JUL 15 2018.
• Citações Web of Science: 0

Resumo

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. (AU)

• Processo FAPESP: 11/12079-5 - Representações de Álgebras de Kac-Moody e grupos quânticos
• Beneficiário: Evan Andrew Wilson
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 15/22040-0 - Aspectos estruturais e representações de álgebras de Kac-Moody, suas generalizações e hiperálgebras
• Beneficiário: Angelo Calil Bianchi
• Modalidade de apoio: Auxílio à Pesquisa - Regular