Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Actions of the derived group of a maximal unipotent subgroup on
  $G$-varieties   Let $U$ be a maximal unipotent subgroup of a connected semisimple group $G$
and $U'$ the derived group of $U$. We study actions of $U'$ on affine
$G$-varieties.
  First, we consider the algebra of $U'$ invariants on $G/U$. We prove that
$k[G/U]^{U'}$ is a polynomial algebra of Krull dimension $2r$, where $r=rk(G)$.
A related result is that, for any simple finite-dimensional $G$-module $V$,
$V^{U'}$ is a cyclic $U/U'$-module.
  Second, we study "symmetries" of Poincare series for $U'$-invariants on
affine conical $G$-varieties.
  Third, we obtain a classification of simple $G$-modules $V$ with polynomial
algebras of $U'$-invariants (for $G$ simple).

13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg