Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conformally invariant differential operators on Heisenberg groups and
  minimal representations   For a simple real Lie group $G$ with Heisenberg parabolic subgroup $P$, we
study the corresponding degenerate principal series representations. For a
certain induction parameter the kernel of the conformally invariant system of
second order differential operators constructed by Barchini, Kable and Zierau
is a subrepresentation which turns out to be the minimal representation. To
study this subrepresentation, we take the Heisenberg Fourier transform in the
non-compact picture and show that it yields a new realization of the minimal
representation on a space of $L^2$-functions. The Lie algebra action is given
by differential operators of order $\leq3$ and we find explicit formulas for
the lowest $K$-type.
  These $L^2$-models were previously known for the groups
$\operatorname{SO}(n,n)$, $E_{6(6)}$, $E_{7(7)}$ and $E_{8(8)}$ by Kazhdan and
Savin, for the group $G_{2(2)}$ by Gelfand, for the group
$\widetilde{\operatorname{SL}}(3,\mathbb{R})$ by Torasso, and for
$\widetilde{\operatorname{SO}}(4,3)$ by Sabourin. Our new approach provides a
uniform and systematic treatment of these cases and also gives new $L^2$-models
for $E_{6(2)}$, $E_{7(-5)}$ and $E_{8(-24)}$ for which the minimal
representation is a continuation of the quaternionic discrete series, and for
the groups $\widetilde{\operatorname{SO}}(p,q)$ with either $p\geq q=3$ or
$p,q\geq4$ and $p+q$ even.

28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga