Bernstein components via the Bernstein center

Alexander Braverman; David Kazhdan

doi:10.1007/s00029-016-0277-3

Bernstein components via the Bernstein center

Alexander Braverman^*
, David Kazhdan

^*Corresponding author for this work

Einstein Institute of Mathematics

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

1 Scopus citations

Abstract

Let G be a reductive p-adic group. Let Φ be an invariant distribution on G lying in the Bernstein center Z(G). We prove that Φ is supported on compact elements in G if and only if it defines a constant function on every component of the set Irr (G) ; in particular, we show that the space of all elements of Z(G) supported on compact elements is a subalgebra of Z(G). Our proof is a slight modification of the argument from Section 2 of Dat (J Reine Angew Math 554:69–103, 2003), where our result is proved in one direction.

Original language	English
Pages (from-to)	2313-2323
Number of pages	11
Journal	Selecta Mathematica, New Series
Volume	22
Issue number	4
DOIs	https://doi.org/10.1007/s00029-016-0277-3
State	Published - 1 Oct 2016

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing.

Keywords

20G05
20G25
22E35
22E50

Access to Document

10.1007/s00029-016-0277-3

Cite this

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title = "Bernstein components via the Bernstein center",

abstract = "Let G be a reductive p-adic group. Let Φ be an invariant distribution on G lying in the Bernstein center Z(G). We prove that Φ is supported on compact elements in G if and only if it defines a constant function on every component of the set Irr (G) ; in particular, we show that the space of all elements of Z(G) supported on compact elements is a subalgebra of Z(G). Our proof is a slight modification of the argument from Section 2 of Dat (J Reine Angew Math 554:69–103, 2003), where our result is proved in one direction.",

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AU - Kazhdan, David

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AB - Let G be a reductive p-adic group. Let Φ be an invariant distribution on G lying in the Bernstein center Z(G). We prove that Φ is supported on compact elements in G if and only if it defines a constant function on every component of the set Irr (G) ; in particular, we show that the space of all elements of Z(G) supported on compact elements is a subalgebra of Z(G). Our proof is a slight modification of the argument from Section 2 of Dat (J Reine Angew Math 554:69–103, 2003), where our result is proved in one direction.

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Bernstein components via the Bernstein center

Abstract

Bibliographical note

Keywords

Access to Document

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Fingerprint

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

Bernstein components via the Bernstein center

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