Geometric structure in smooth dual and local Langlands conjecture
Geometric structure in smooth dual and local Langlands conjecture
This expository paper first reviews some basic facts about p-adic fields, reductive p-adic groups, and the local Langlands conjecture. If G is a reductive p-adic group, then the smooth dual of G is the set of equivalence classes of smooth irreducible representations of G. The representations are on vector spaces over the complex numbers. In a canonical way, the smooth dual is the disjoint union of subsets known as the Bernstein components. According to a conjecture due to ABPS (Aubert–Baum–Plymen–Solleveld), each Bernstein component has a geometric structure given by an appropriate extended quotient. The paper states this ABPS conjecture and then indicates evidence for the conjecture, and its connection to the local Langlands conjecture.
99-136
Aubert, Anne-Marie
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Baum, Paul
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Plymen, Roger
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Solleveld, Maarten
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Aubert, Anne-Marie
f1ab184a-28bd-49a7-bec5-d0abcec2fed0
Baum, Paul
fb630982-847c-4fef-8bd3-b344875be774
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Solleveld, Maarten
87e40b53-0137-45fd-8582-38da531528a4
Aubert, Anne-Marie, Baum, Paul, Plymen, Roger and Solleveld, Maarten
(2014)
Geometric structure in smooth dual and local Langlands conjecture.
Japanese Journal of Mathematics, 9 (2), .
(doi:10.1007/s11537-014-1267-x).
Abstract
This expository paper first reviews some basic facts about p-adic fields, reductive p-adic groups, and the local Langlands conjecture. If G is a reductive p-adic group, then the smooth dual of G is the set of equivalence classes of smooth irreducible representations of G. The representations are on vector spaces over the complex numbers. In a canonical way, the smooth dual is the disjoint union of subsets known as the Bernstein components. According to a conjecture due to ABPS (Aubert–Baum–Plymen–Solleveld), each Bernstein component has a geometric structure given by an appropriate extended quotient. The paper states this ABPS conjecture and then indicates evidence for the conjecture, and its connection to the local Langlands conjecture.
Text
Takagi13.pdf
- Accepted Manuscript
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Accepted/In Press date: 14 February 2014
e-pub ahead of print date: 23 May 2014
Organisations:
Pure Mathematics
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Local EPrints ID: 369696
URI: http://eprints.soton.ac.uk/id/eprint/369696
ISSN: 0289-2316
PURE UUID: f1f66593-a16c-49f4-a962-473d7ccac62f
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Date deposited: 09 Oct 2014 12:59
Last modified: 14 Mar 2024 18:07
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Author:
Anne-Marie Aubert
Author:
Paul Baum
Author:
Maarten Solleveld
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