Is there a standard notation for off-diagonal transpose?

In http://arxiv.org/abs/math/0701936 (Fuchsian equations of type DN, by Vasily Golyshev and Jan Stienstra) the transpose of the matrix $A$ with respect to the anti-diagonal is denoted by $A^\tau$. It relates to the ordinary transpose $A^T$ (or $A^t$ as used in the paper), as follows: $$A^\tau=JA^TJ$$ where $J=(J_{ij})_{0\le i,j\le n}$ denotes the matrix with $J_{ij}=1$ if $i+j=n$ and $J_{ij}=0$ otherwise. This fact was already noted by Pietro Majer for the case $n=1$ with notation $P$ instead of $J$ used in the Golyshev and Stienstra paper.