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

Author(s)

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

Affiliation

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

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

• Document type: Journal article
• Source: Journal of Algebra; v. 506, p. 509-539, JUL 15 2018.
• Web of Science Citations: 0

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. (AU)

• FAPESP's process: 11/12079-5 - Representations of Kac-Moody Algebras and quantum groups
• Grantee: Evan Andrew Wilson
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 14/09310-5 - Algebraic structures and their representations
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 15/22040-0 - Structural aspects and representations of Kac-Moody algebras, their generalizations and hyperalgebras
• Grantee: Angelo Calil Bianchi
• Support Opportunities: Regular Research Grants