  In 2011, Han and Ji proved addition-multiplication theorems for integer
partitions, from which they derived modular analogues of many classical
identities involving hook-length. In the present paper, we prove
addition-multiplication theorems for the subset of self-conjugate partitions.
Although difficulties arise due to parity questions, we are almost always able
to include the BG-rank introduced by Berkovich and Garvan. This gives us as
consequences many self-conjugate modular versions of classical hook-lengths
identities for partitions. Our tools are mainly based on fine properties of the
Littlewood decomposition restricted to self-conjugate partitions.
