In a highest weight category, ''decomposition numbers'' refers to multiplicities of simple objects in standard objects. I will describe results that are known about decomposition numbers for Category O of a rational Cherednik algebra, and mention some questions that remain open.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/4234
[3] http://www.mpim-bonn.mpg.de/node/6971