2010.70: Geometric structure in the principal series of the p-adic group G_2
2010.70: Anne-Marie Aubert, Paul Baum and Roger Plymen (2010) Geometric structure in the principal series of the p-adic group G_2. Representation Theory.
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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 , 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 $G_2$.
A feature of this article is the role played by cocharacters $h_c$ 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 correction, 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 correction is controlled by the cocharacters $h_c$. The cocharacters themselves appear to be closely related to Langlands parameters.
To appear in Representation Theory, an electronic journal published by the American Mathematical Society
|Uncontrolled Keywords:||Geometric structure, principal series, cocharacters|
|Subjects:||MSC 2000 > 20 Group theory and generalizations|
MSC 2000 > 22 Topological groups, Lie groups
|Deposited By:||Professor Roger Plymen|
|Deposited On:||07 August 2010|