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Geometric structure in the principal series of the p-adic group G_2

Geometric structure in the principal series of the p-adic group G_2
Geometric structure in the principal series of the p-adic group G_2
In the representation theory of reductive -adic groups , the issue of reducibility of induced representations is an issue of great intricacy. It is our contention, expressed as a conjecture in (2007), that there exists a simple geometric structure underlying this intricate theory.

We will illustrate here the conjecture with some detailed computations in the principal series of .

A feature of this article is the role played by cocharacters attached to two-sided cells in certain extended affine Weyl groups.

The quotient varieties which occur in the Bernstein programme are replaced by extended quotients. We form the disjoint union of all these extended quotient varieties. We conjecture that, after a simple algebraic deformation, the space is a model of the smooth dual . In this respect, our programme is a conjectural refinement of the Bernstein programme.

The algebraic deformation is controlled by the cocharacters . The cocharacters themselves appear to be closely related to Langlands parameters.

1088-4165
126-169
Aubert, Anne-Marie
f1ab184a-28bd-49a7-bec5-d0abcec2fed0
Baum, Paul
fb630982-847c-4fef-8bd3-b344875be774
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Aubert, Anne-Marie
f1ab184a-28bd-49a7-bec5-d0abcec2fed0
Baum, Paul
fb630982-847c-4fef-8bd3-b344875be774
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5

Aubert, Anne-Marie, Baum, Paul and Plymen, Roger (2011) Geometric structure in the principal series of the p-adic group G_2. Representation Theory, 15, 126-169. (doi:10.1090/S1088-4165-2011-00392-7).

Record type: Article

Abstract

In the representation theory of reductive -adic groups , the issue of reducibility of induced representations is an issue of great intricacy. It is our contention, expressed as a conjecture in (2007), that there exists a simple geometric structure underlying this intricate theory.

We will illustrate here the conjecture with some detailed computations in the principal series of .

A feature of this article is the role played by cocharacters attached to two-sided cells in certain extended affine Weyl groups.

The quotient varieties which occur in the Bernstein programme are replaced by extended quotients. We form the disjoint union of all these extended quotient varieties. We conjecture that, after a simple algebraic deformation, the space is a model of the smooth dual . In this respect, our programme is a conjectural refinement of the Bernstein programme.

The algebraic deformation is controlled by the cocharacters . The cocharacters themselves appear to be closely related to Langlands parameters.

Full text not available from this repository.

More information

Published date: February 2011
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 176139
URI: https://eprints.soton.ac.uk/id/eprint/176139
ISSN: 1088-4165
PURE UUID: 35826c72-cb5e-4fa4-ad00-e5102dccc9e5

Catalogue record

Date deposited: 03 Mar 2011 15:52
Last modified: 16 Jul 2019 23:46

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