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math.RTSep 1, 2014
41
citations (OpenAlex)
authors
  • Vyacheslav Futorny
  • Dimitar Grantcharov
  • Luis Enrique Ramirez
institutions
  • Universidade de São Paulo
arXiv abstractPDF
paper

Irreducible Generic Gelfand-Tsetlin Modules of gl(n)

arXiv:1409.8413 · doi:10.3842/SIGMA.2015.018

Abstract

We provide a classification and explicit bases of tableaux of all irreducible generic Gelfand-Tsetlin modules for the Lie algebra gl(n).

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  • New singular Gelfand-Tsetlin gl(n)-modules of index 2
  • New family of simple gl2n​(C)-modules
  • Combinatorial construction of Gelfand-Tsetlin modules for gln​
  • Gelfand-Tsetlin modules over gl(n,C) with arbitrary characters
  • Irreducible subquotients of generic gelfand-tsetlin modules over uq(gl(n))
  • Families of irreducible singular Gelfand-Tsetlin modules of gl(n)
  • Gelfand-Tsetlin modules of quantum gl_n$defined by admissible sets of relations
  • Explicit construction of irreducible modules for U_q(gl_n)
  • Relationships Between Mutations of Brauer Configuration Algebras and Some Diophantine Equations
  • The Gelfand-Tsetlin Realisation of Simple Modules and Monomial Bases
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