Skip to Main Content

Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Geometric structure in the principal series of the $p$-adic group $\textrm {G}_2$
HTML articles powered by AMS MathViewer

by Anne-Marie Aubert, Paul Baum and Roger Plymen
Represent. Theory 15 (2011), 126-169
Published electronically: February 23, 2011


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 $\textrm {G}_2$.

A feature of this article is the role played by cocharacters $h_{\mathbf {c}}$ attached to two-sided cells $\mathbf {c}$ 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 $\mathfrak {A}(G)$ of all these extended quotient varieties. We conjecture that, after a simple algebraic deformation, the space $\mathfrak {A}(G)$ is a model of the smooth dual $\textrm {Irr}(G)$. In this respect, our programme is a conjectural refinement of the Bernstein programme.

The algebraic deformation is controlled by the cocharacters $h_{\mathbf {c}}$. The cocharacters themselves appear to be closely related to Langlands parameters.

Similar Articles
  • Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 20G05, 22E50
  • Retrieve articles in all journals with MSC (2010): 20G05, 22E50
Bibliographic Information
  • Anne-Marie Aubert
  • Affiliation: Institut de Mathématiques de Jussieu, U.M.R. 7586 du C.N.R.S. and U.P.M.C., 75005 Paris, France
  • MR Author ID: 256498
  • ORCID: 0000-0002-9613-9140
  • Email:
  • Paul Baum
  • Affiliation: Pennsylvania State University, Mathematics Department, University Park, Pennsylvania 16802
  • MR Author ID: 32700
  • Email:
  • Roger Plymen
  • Affiliation: School of Mathematics, Alan Turing building, Manchester University, Manchester M13 9PL, England
  • Email:
  • Received by editor(s): July 14, 2009
  • Received by editor(s) in revised form: May 27, 2010, and June 17, 2010
  • Published electronically: February 23, 2011
  • Additional Notes: The second author was partially supported by NSF grant DMS-0701184
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 15 (2011), 126-169
  • MSC (2010): Primary 20G05, 22E50
  • DOI:
  • MathSciNet review: 2772586