Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Double cosets $NgN$ of normalizers of maximal tori of simple algebraic
  groups and orbits of partial actions of Cremona subgroups   Let $G$ be a simple algebraic group over an algebraically closed field $K$
and let $N = N_G(T)$ be the normalizer of a fixed maximal torus $T\leq G$.
Further, let $U$ be the unipotent radical of a fixed Borel subgroup $B$ that
contains $T$ and let $U^-$ be the unipotent radical of the opposite Borel
subgroup $B^-$. The Bruhat decomposition implies the decomposition $G =
NU^-UN$. The Zariski closed subset $U^-U\subset G$ is isomorphic to the affine
space $A_K^m$ where $m = \dim G -\dim T$ is the number of roots in the
corresponding root system. Here we construct a subgroup $\mathcal{N}\leq
\operatorname{Cr}_m(K)$ that ``acts partially'' on $A_K^m\approx\mathcal{U}$
and we show that there is one-to-one correspondence between the orbits of such
a partial action and the set of double cosets $\{NgN\}$. Here we also calculate
the set $\{g_\alpha\}_{\alpha \in \mathfrak A}\subset \mathcal{U}$ in the
simplest case $G = \operatorname{SL}_2(\mathbb{C})$.

15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg