Irreducible representations of the plactic algebra of rank four

Ferran Cedó, Łukasz Kubat, Jan Okniński

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1 Citation (Scopus)

Abstract

© 2016 Elsevier Inc. Irreducible representations of the plactic monoid M of rank four are studied. Certain concrete families of simple modules over the plactic algebra K[M] over a field K are constructed. It is shown that the Jacobson radical J(K[M]) of K[M] is nilpotent. Moreover, the congruence ρ on M determined by J(K[M]) coincides with the intersection of the congruences determined by the primitive ideals of K[M] corresponding to the constructed simple modules. In particular, M/ρ is a subdirect product of the images of M in the corresponding endomorphism algebras.
Original languageEnglish
Pages (from-to)403-441
JournalJournal of Algebra
Volume488
DOIs
Publication statusPublished - 15 Oct 2017

Keywords

  • Irreducible representation
  • Jacobson radical
  • Plactic algebra
  • Plactic monoid
  • Simple module

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