Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Action of Weyl group on zero weight space   For any simple complex Lie group we classify irreducible finite-dimensional
representations $\rho$ for which the longest element $w_0$ of the Weyl group
acts nontrivially on the zero weight space. Among irreducible representations
that have zero among their weights, $w_0$ acts by $\pm$Id if and only if the
highest weight of $\rho$ is a multiple of a fundamental weight, with a
coefficient less than a bound that depends on the group and on the fundamental
weight.

3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph