This is explained in section 8 of the document:7. Juli 2015 01:46[I do not get copies from the list, though having signed up.]
The spacing is different in cases - TeX also has such a variation. Specifically, there is extra space before the conditionals.
In addition, it seems \startmathcases ... \stopmathcases is not working with UTF-8: in the example below, the ω’s on the second line, after the arrows, disappear in my PDF.
Please send always working minimal examples like this:----
\startformula
J^j:\startmathcases\NC ω^0 \NC→ 0 \NR \NC ω^j \NC→ 0 \stopmathcases \quad
\startmathcases \NC ω^k \NC→ ω^l \NR \NC ω^l \NC→ -ω^k \stopmathcases
\stopformula
----