Kirillov models and integral structures in p-adic smooth representations of GL 2(F)

David Kazhdan, Ehud de Shalit

Research output: Contribution to journalArticlepeer-review

Abstract

Let F be a local field of residual characteristic p, and ρ a smooth irreducible representation of GL 2(F), realized over the algebraic closure of Qp. Studying its Kirillov model, we exhibit a necessary and sufficient criterion for the existence of an integral structure in ρ. We apply our criterion to tamely ramified principal series, and get a new proof of a theorem of M.-F. Vigneras.

Original languageAmerican English
Pages (from-to)212-223
Number of pages12
JournalJournal of Algebra
Volume353
Issue number1
DOIs
StatePublished - 1 Mar 2012

Keywords

  • Integral structures
  • Smooth representations

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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