Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Aligned SICs and embedded tight frames in even dimensions   Alignment is a geometric relation between pairs of Weyl-Heisenberg SICs, one
in dimension $d$ and another in dimension $d(d-2)$, manifesting a well-founded
conjecture about a number-theoretical connection between the SICs. In this
paper, we prove that if $d$ is even, the SIC in dimension $d(d-2)$ of an
aligned pair can be partitioned into $(d-2)^2$ tight $d^2$-frames of rank
$d(d-1)/2$ and, alternatively, into $d^2$ tight $(d-2)^2$-frames of rank
$(d-1)(d-2)/2$. The corresponding result for odd $d$ is already known, but the
proof for odd $d$ relies on results which are not available for even $d$. We
develop methods that allow us to overcome this issue. In addition, we provide a
relatively detailed study of parity operators in the Clifford group,
emphasizing differences in the theory of parity operators in even and odd
dimensions and discussing consequences due to such differences. In a final
section, we study implications of alignment for the symmetry of the SIC.

24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin