Gelfand-Tsetlin modules of quantum gl(n) defined by admissible sets of relations

Author(s)

Futorny, Vyacheslav ^[1] ; Ramirez, Luis Enrique ^[2] ; Zhang, Jian ^[1]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo, SP - Brazil

^[2] Univ Fed ABC, Santo Andre, SP - Brazil

• Document type: Journal article
• Source: Journal of Algebra; v. 499, p. 375-396, APR 1 2018.
• Web of Science Citations: 0

Abstract

The purpose of this paper is to construct new families of irreducible Gelfand Tsetlin modules for U-q(gl(n)) These modules have arbitrary singularity and Gelfand-Tsetlin multiplicities bounded by 2. Most previously known irreducible modules had all Gelfand-Tsetlin multiplicities bounded by 1 {[}16], {[}17]. In particular, our method provides new families of irreducible Gelfand Tsetlin modules for gl(n). This generalizes the results of {[}10] and {[}15]. (C) 2017 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: 15/05927-0 - Quantum determinants and categorification of quantum groups
• Grantee: Jian Zhang
• Support Opportunities: Scholarships in Brazil - Post-Doctoral