Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of multiplicity free symplectic representations   Let G be a connected reductive group acting on a finite dimensional vector
space V. Assume that V is equipped with a G-invariant symplectic form. Then the
ring C[V] of polynomial functions becomes a Poisson algebra. The ring C[V]^G of
invariants is a sub-Poisson algebra. We call V multiplicity free if C[V]^G is
Poisson commutative, i.e., if {f,g}=0 for all invariants f and g.
Alternatively, G also acts on the Weyl algebra W(V) and V is multiplicity free
if and only if the subalgebra W(V)^G of invariants is commutative. In this
paper we classify all multiplicity free symplectic representations.

12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph