I'm looking at the induction of representations of a parabolic subgroup of $Sp_4$ into the whole group. There are some cases that the result is reducible, and I need to compute the dimensions of the subrepresentations. So I was wondering if there is a general procedure to compute the dimensions, like there is a pretty general procedure to check irreducibility - i.e. Mackey's criterion (which is how I found the cases that are reducible).
My question: if an induced representation is reducible, is there a relatively general method to compute the dimensions of the subrepresentations?
I should be able to do my specific example by reading the existing literature on $Sp_4$, but the articles I have read so far (B. Srinivasan, T. A. Springer) don't say how they figured out the dimensions.
