Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orbit Functions   In the paper, properties of orbit functions are reviewed and further
developed. Orbit functions on the Euclidean space $E_n$ are symmetrized
exponential functions. The symmetrization is fulfilled by a Weyl group
corresponding to a Coxeter-Dynkin diagram. Properties of such functions will be
described. An orbit function is the contribution to an irreducible character of
a compact semisimple Lie group $G$ of rank $n$ from one of its Weyl group
orbits. It is shown that values of orbit functions are repeated on copies of
the fundamental domain $F$ of the affine Weyl group (determined by the initial
Weyl group) in the entire Euclidean space $E_n$. Orbit functions are solutions
of the corresponding Laplace equation in $E_n$, satisfying the Neumann
condition on the boundary of $F$. Orbit functions determine a symmetrized
Fourier transform and a transform on a finite set of points.

34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol