A spectral decomposition of orbital integrals for PGL(2, F) (with an appendix by S. Debacker)

David Kazhdan

doi:10.1007/s00029-017-0321-y

A spectral decomposition of orbital integrals for PGL(2, F) (with an appendix by S. Debacker)

David Kazhdan^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

1 Scopus citations

Abstract

Let F be a local non-archimedian field, G a semisimple F-group, dg a Haar measure on G and S(G) be the space of locally constant complex valued functions f on G with compact support. For any regular elliptic congugacy class Ω = h^G⊂ G we denote by I_Ω the G-invariant functional on S(G) given by (Formula presented.) This paper provides the spectral decomposition of functionals I_Ω in the case G= PGL (2 , F) and in the last section first steps of such an analysis for the general case.

Original language	English
Pages (from-to)	473-497
Number of pages	25
Journal	Selecta Mathematica, New Series
Volume	24
Issue number	1
DOIs	https://doi.org/10.1007/s00029-017-0321-y
State	Published - 1 Mar 2018

Bibliographical note

Publisher Copyright:
© 2017, Springer International Publishing.

Keywords

22E50

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10.1007/s00029-017-0321-y

Cite this

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N2 - Let F be a local non-archimedian field, G a semisimple F-group, dg a Haar measure on G and S(G) be the space of locally constant complex valued functions f on G with compact support. For any regular elliptic congugacy class Ω = hG⊂ G we denote by IΩ the G-invariant functional on S(G) given by (Formula presented.) This paper provides the spectral decomposition of functionals IΩ in the case G= PGL (2 , F) and in the last section first steps of such an analysis for the general case.

AB - Let F be a local non-archimedian field, G a semisimple F-group, dg a Haar measure on G and S(G) be the space of locally constant complex valued functions f on G with compact support. For any regular elliptic congugacy class Ω = hG⊂ G we denote by IΩ the G-invariant functional on S(G) given by (Formula presented.) This paper provides the spectral decomposition of functionals IΩ in the case G= PGL (2 , F) and in the last section first steps of such an analysis for the general case.

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A spectral decomposition of orbital integrals for PGL(2, F) (with an appendix by S. Debacker)

Abstract

Bibliographical note

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Correction to: Acknowledgments in six articles published in Selecta Mathematica (Selecta Mathematica, (2018), 24, 1, (473-497), 10.1007/s00029-017-0321-y)

Cite this

A spectral decomposition of orbital integrals for PGL(2, F) (with an appendix by S. Debacker)

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Related research output

Correction to: Acknowledgments in six articles published in Selecta Mathematica (Selecta Mathematica, (2018), 24, 1, (473-497), 10.1007/s00029-017-0321-y)

Cite this