Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the isomorphism of certain primitive $Q$-polynomial not
  $P$-polynomial association schemes   In 2011, Penttila and Williford constructed an infinite new family of
primitive $Q$-polynomial 3-class association schemes, not arising from distance
regular graphs, by exploring the geometry of the lines of the unitary polar
space $H(3,q^2)$, $q$ even, with respect to a symplectic polar space $W(3,q)$
embedded in it.
  In a private communication to Penttila and Williford, H.~Tanaka pointed out
that these schemes have the same parameters as the 3-class schemes found by
Hollmann and Xiang in 2006 by considering the action of $\mathrm{PGL}(2,q^2)$,
$q$ even, on a non-degenerate conic of $\mathrm{PG}(2,q^2)$ extended in
$\mathrm{PG}(2,q^4)$. Therefore, the question arises whether the above
association schemes are isomorphic. In this paper we provide the positive
answer. As by product, we get an isomorphism of strongly regular graphs.

33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat