Cyclic representations of general linear p-adic groups

Maxim Gurevich, Alberto Mínguez

Research output: Contribution to journalArticlepeer-review


Let π1,…,πk be smooth irreducible representations of p-adic general linear groups. We prove that the parabolic induction product π1×⋯×πk has a unique irreducible quotient whose Langlands parameter is the sum of the parameters of all factors (cyclicity property), assuming that the same property holds for each of the products πi×πj (i<j), and that for all but at most two representations πi×πi remains irreducible (square-irreducibility property). Our technique applies the recently devised Kashiwara-Kim notion of a normal sequence of modules for quiver Hecke algebras. Thus, a general cyclicity problem is reduced to the recent Lapid-Mínguez conjectures on the maximal parabolic case.

Original languageEnglish
Pages (from-to)25-35
Number of pages11
JournalJournal of Algebra
StatePublished - 1 Nov 2021


  • Categorical equivalences
  • Irreducibility criteria
  • Langlands classification
  • Representation theory
  • p-adic groups

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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