Singularities of intertwining operators and decompositions of principal series representations

Taeuk Nam, Avner Segal, Lior Silberman

Research output: Contribution to journalArticlepeer-review


We show that, under certain assumptions, a parabolic induction IndGB λ from the Borel subgroup B of a (real or p-adic) reductive group G decomposes into a direct sum of the form: IndGB λ = ( IndGP StM ⊗χ0 ) ⊕ ( IndGP 1M ⊗χ0 ), where P is a parabolic subgroup of G with Levi subgroup M of semi-simple rank 1, 1M is the trivial representation of M, StM is the Steinberg representation of M and χ0 is a certain character of M. We construct examples of this phenomenon for all simply-connected simple groups of rank at least 2.

Original languageEnglish
Pages (from-to)939-964
Number of pages26
JournalJournal of Lie Theory
Issue number4
StatePublished - 1 Jan 2020
Externally publishedYes


  • Intertwining operators
  • Lie groups
  • P-adic groups
  • Principle series
  • Representation theory

ASJC Scopus subject areas

  • Algebra and Number Theory


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