Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric structure in the principal series of the p-adic group G_2   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
$G_2$.
  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 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 $h_c$, one for each
two-sided cell $c$ in certain extended affine Weyl groups. The cocharacters
themselves appear to be closely related to Langlands parameters.

35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat