Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Hamiltonian Reduction for Polar Representations   Let $G$ be a reductive complex Lie group with Lie algebra $\mathfrak{g}$ and
suppose that $V$ is a polar $G$-representation. We prove the existence of a
radial parts map $\mathrm{rad}: \mathcal{D}(V)^G\to A_{\kappa}$ from the
$G$-invariant differential operators on $V$ to the spherical subalgebra
$A_{\kappa}$ of a rational Cherednik algebra. Under mild hypotheses
$\mathrm{rad}$ is shown to be surjective.
  If $V$ is a symmetric space, then $\mathrm{rad}$ is always surjective, and we
determine exactly when $A_{\kappa}$ is a simple ring. When $A_{\kappa}$ is
simple, we also show that the kernel of $\mathrm{rad}$ is
$\left(\mathcal{D}(V)\tau(\mathfrak{g}\right)^G$, where $\tau:\mathfrak{g}\to
\mathcal{D}(V)$ is the differential of the $G$-action.

26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat