New families of irreducible weight modules over sl(3)

Author(s)

Futorny, Vyacheslav ^[1] ; Liu, Genqiang ^[2] ; Lu, Rencai ^[3] ; Zhao, Kaiming ^{[4, 5]}

Affiliation

^[1] Univ Sao Paulo, Inst Math & Stat, BR-05315970 Sao Paulo - Brazil

^[2] Henan Univ, Sch Math & Stat, Kaifeng 475004 - Peoples R China

^[3] Soochow Univ, Dept Math, Suzhou - Peoples R China

^[4] Hebei Normal Teachers Univ, Coll Math & Informat Sci, Shijiazhuang 050016, Hebei - Peoples R China

^[5] Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5 - Canada

• Document type: Journal article
• Source: Journal of Algebra; v. 501, p. 458-472, MAY 1 2018.
• Web of Science Citations: 0

Abstract

Let n > 1 be an integer, alpha is an element of C-n, b is an element of C, and V a gl(n)-module. We define a class of weight modules F-b(alpha) (V) over sl(n+1) using the restriction of modules of tensor fields over the Lie algebra of vector fields on n-dimensional torus. In this paper we consider the case n = 2 and prove the irreducibility of such 5-parameter sl(3)-modules F-b(alpha) (V) generically. All such modules have infinite dimensional weight spaces and lie outside of the category of Gelfand-Tsetlin modules. Hence, this construction yields new families of irreducible sl(3)-modules. (C) 2018 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 14/09310-5 - Algebraic structures and their representations
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 15/08615-0 - Simple representations of Witt and Kac-Moody algebras
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Grants - Visiting Researcher Grant - International