Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On complete reducibility of tensor products of simple modules over
  simple algebraic groups   Let $G$ be a simply connected simple algebraic group over an algebraically
closed field $k$ of characteristic $p>0$. The category of rational $G$-modules
is not semisimple. We consider the question of when the tensor product of two
simple $G$-modules $L(\lambda)$ and $L(\mu)$ is completely reducible. Using
some technical results about weakly maximal vectors (i.e. maximal vectors for
the action of the Frobenius kernel $G_1$ of $G$) in tensor products, we obtain
a reduction to the case where the highest weights $\lambda$ and $\mu$ are
$p$-restricted. In this case, we also prove that $L(\lambda)\otimes L(\mu)$ is
completely reducible as a $G$-module if and only if $L(\lambda)\otimes L(\mu)$
is completely reducible as a $G_1$-module.

31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph