Explicit construction of irreducible modules for \(U_q(\mathfrak {gl}_n)\)

  • Vyacheslav FutornyEmail author
  • Luis Enrique Ramirez
  • Jian Zhang


We construct new families of \(U_q(\mathfrak {gl}_n)\)-modules by continuation from finite dimensional representations. Each such module is associated with a combinatorial object—admissible set of relations. More precisely, we prove that any admissible set of relations leads to a family of irreducible \(U_q(\mathfrak {gl}_n)\)-modules. Finite dimensional and generic modules are particular cases of this construction.


Quantum group Gelfand–Tsetlin module Gelfand–Tsetlin basis Tableaux realization 

Mathematics Subject Classification

Primary 17B67 



V.F. is supported in part by CNPq (304467/2017-0) and by Fapesp (2014/09310-5). L.E.R. is supported by Fapesp (2018/17955-7) and J. Z. is supported by Fapesp (2015/05927-0).

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest


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Copyright information

© Instituto de Matemática e Estatística da Universidade de São Paulo 2019

Authors and Affiliations

  1. 1.Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil
  2. 2.Universidade Federal do ABCSanto AndréBrazil

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