I am a pure mathematician interested in representation theory.
I computed $q$-characters of $\ell$-fundamental representations for the quantum affine $E_8$ by a SUPERCOMPUTER. See
There is more famous project on $E_8$:
I believe there are lots of other computation in the representation theory of exceptional groups, which require lots of memory.
They are usually based on recursive algorithms, and one cannot use the parallel computing.
When I computed $q$-characters, I could not find any guides explaining how to code a program for such a problem. I appreciate very much if an expert could give me any references.