TITLE: Automorphic forms on GL(3)
QUESTION [10 upvotes]: We know that the classical Maass forms on GL(3) are depicted, for instance, in D.Goldfeld's book. I wonder that if there exists "holomorphic" automorphic forms on GL(3) as an analogue of GL(2) case. If those forms exist, where can I find the materials which concretely tell the story of them?
Thanks in advance.

REPLY [3 votes]: Slightly old question, but:  There are Maass forms on GL(3) whose minimal K-type is non-spherical.  There is a paper of Miyazaki on the (g,K) module structure of GL(3), and I'm working on a more complete description.