Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Oscillator algebras with semi-equicontinuous coadjoint orbits   A unitary representation of a, possibly infinite dimensional, Lie group G is
called semi-bounded if the corresponding operators id\pi(x) from the derived
representations are uniformly bounded from above on some non-empty open subset
of the Lie algebra g. Not every Lie group has non-trivial semibounded unitary
representations, so that it becomes an important issue to decide when this is
the case. In the present paper we describe a complete solution of this problem
for the class of generalized oscillator groups, which are semidirect products
of Heisenberg groups with a one-parameter group \gamma. For these groups it
turns out that the existence of non-trivial semibounded representations is
equivalent to the existence of so-called semi-equicontinuous non-trivial
coadjoint orbits, a purely geometric condition on the coadjoint action. This in
turn can be expressed by a positivity condition on the Hamiltonian function
corresponding to the infinitesimal generator D of \gamma. A central point of
our investigations is that we make no assumption on the structure of the
spectrum of D. In particular, D can be any skew-adjoint operator on a Hilbert
space.

37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph