Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orthogonal determinants of characters   For an irreducible orthogonal character $\chi $ of even degree there is a
unique square class $\det({\chi })$ in the character field such that the
invariant quadratic forms in any $L$-representation affording $\chi $ have
determinant in $\det({\chi })(L^*)^2$.

35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org