Cyclic odd degree base change lifting for unitary groups in three variables

Ping Shun Chan, Yuval Z. Flicker

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Let F be a number field or a p-adic field of odd residual characteristic. Let E be a quadratic extension of F, and F′ an odd degree cyclic field extension of F. We establish a base-change functorial lifting of automorphic (respectively, admissible) representations from the unitary group U(3, E/F) to the unitary group U(3, F′ E/F′). As a consequence, we classify, up to certain restrictions, the packets of U(3, F′ E/F′) which contain irreducible automorphic (respectively, admissible) representations invariant under the action of the Galois group Gal(F′ E/E). We also determine the invariance of individual representations. This work is the first study of base change into an algebraic group whose packets are not all singletons, and which does not satisfy the rigidity, or 'strong multiplicity one', theorem. Novel phenomena are encountered: e.g. there are invariant packets where not every irreducible automorphic (respectively, admissible) member is Galois-invariant. The restriction that the residual characteristic of the local fields be odd may be removed once the multiplicity one theorem for U(3) is proved to hold unconditionally without restriction on the dyadic places.

Original languageEnglish
Pages (from-to)1247-1309
Number of pages63
JournalInternational Journal of Number Theory
Issue number7
StatePublished - Nov 2009
Externally publishedYes


  • Automorphic representations
  • Base change
  • Langlands functoriality
  • Trace formula
  • Unitary groups


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