Multiplicity formula for restriction of representations of GL2(F) to SL2(F)

Shiv Prakash Patel, Dipendra Prasad

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In this note we prove a certain multiplicity formula regarding the restriction of an irreducible admissible genuine representation of a 2-fold cover GL2(F) of GL2(F) to the 2-fold cover L2 (F) of SL2 (F), and find in particular that this multiplicity may not be one, a result that was recently observed for certain principal series representations in the work of Szpruch (2013). The proofs follow the standard path via Waldspurger’s analysis of theta correspondence between L2(F) and PGL2(F).

Original languageEnglish
Pages (from-to)903-908
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number2
StatePublished - 1 Feb 2016
Externally publishedYes


  • Covering groups
  • Multiplicity formula
  • Restriction of representations

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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