Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semisimple orbital integrals on the symplectic space for a real
  reductive dual pair   We prove a Weyl Harish-Chandra integration formula for the action of a
reductive dual pair on the corresponding symplectic space $W$. As an
intermediate step, we introduce a notion of a Cartan subspace and a notion of
an almost semisimple element in the symplectic space $W$. We prove that the
almost semisimple elements are dense in $W$. Finally, we provide estimates for
the orbital integrals associated with the different Cartan subspaces in $W$.

10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th