Geometric structure in the principal series of the P-adic group G2

Anne Marie Aubert, Paul Frank Baum, Roger Plymen

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In the representation theory of reductive p-adic groups G, 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 G2. A feature of this article is the role played by cocharacters hc attached to two-sided cells c 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 A(G) of all these extended quotient varieties. We conjecture that, after a simple algebraic deformation, the space A(G) is a model of the smooth dual Irr(G). In this respect, our programme is a conjectural refinement of the Bernstein programme. The algebraic deformation is controlled by the cocharacters hc. The cocharacters themselves appear to be closely related to Langlands parameters.

Original languageEnglish (US)
Pages (from-to)126-169
Number of pages44
JournalRepresentation Theory
Volume15
Issue number4
DOIs
StatePublished - Feb 23 2011

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P-adic Groups
Geometric Structure
Quotient
Series
Affine Weyl Groups
Induced Representations
Reductive Group
Reducibility
Contention
Representation Theory
Disjoint
Union
Refinement
Cell
Model

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

Cite this

Aubert, Anne Marie ; Baum, Paul Frank ; Plymen, Roger. / Geometric structure in the principal series of the P-adic group G2. In: Representation Theory. 2011 ; Vol. 15, No. 4. pp. 126-169.
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Geometric structure in the principal series of the P-adic group G2. / Aubert, Anne Marie; Baum, Paul Frank; Plymen, Roger.

In: Representation Theory, Vol. 15, No. 4, 23.02.2011, p. 126-169.

Research output: Contribution to journalArticle

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