2008/10/03 by Anne‐Marie Aubert, Anne-Marie Aubert, Aubert, Anne-Marie +4 · 2 citations
Mathematics · #20G05 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Combinatorics #Computer science #FOS: Mathematics #Geology #Geometry #Group (periodic table) #Mathematics #Paleontology #Physics #Principal (computer security) #Pure mathematics #Representation Theory (math.RT) #Series (stratigraphy) #advanced mathematical theories #math.RT #msc:20G05 #msc:22E50
paper · pdf · doi:10.48550/arxiv.0810.0638
published in arXiv (Cornell University) (Cornell University) · 44 pages. Final version, containing extra material on the cocharacters. To appear in Representation Theory, published by the American Mathematical Society
openalex publication_date 2008/10/03 · arxiv created 2010/08/04 · arxiv updated 2010/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 [3], 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 cocharacters hc, one for each two-sided cell c in certain extended affine Weyl groups. The cocharacters themselves appear to be closely related to Langlands parameters.