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

Shiv Prakash Patel; Dipendra Prasad

doi:10.1090/proc12721

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

Shiv Prakash Patel, Dipendra Prasad

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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 language	English
Pages (from-to)	903-908
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	144
Issue number	2
DOIs	https://doi.org/10.1090/proc12721
State	Published - 1 Feb 2016
Externally published	Yes

Keywords

Covering groups
Multiplicity formula
Restriction of representations

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/proc12721

Cite this

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title = "Multiplicity formula for restriction of representations of GL2(F) to SL2(F)",

abstract = "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{\textquoteright}s analysis of theta correspondence between L2(F) and PGL2(F).",

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AU - Prasad, Dipendra

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N2 - 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).

AB - 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).

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