Carl Solomon! I'm with you in Rockland where you're madder than I am
The speaker declares his solidarity with Carl Solomon, who resides the mental hospital called "Rockland."
In real life, Ginsberg met Solomon at the Columbia Presbyterian Psychiatric Institute, where Solomon was treated for depression with shock therapy (Source).
The speaker is all, "I'm with ya, buddy. We're two peas in a pod…except you're crazier than I am." So maybe not total solidarity, after all.
Then again, being "mad" might be a good thing in this poem.
I'm with you in Rockland where you must feel very strange
The speaker thinks it must feel strange to be living in a mental institution.
He repeats the phrase "I'm with you in Rockland" like a chant or an oath of loyalty.
I'm with you in Rockland where you imitate the shade of my mother
The speaker compares Solomon to the "shade" or ghost of his mother.
Useful information: Ginsberg's mother suffered from mental illness (Source).
I'm with you in Rockland where you've murdered your twelve secretaries
Solomon apparently suffers from delusions. He believes he has murdered his "twelve secretaries." The speaker gives us one example of Solomon's insanity.
I'm with you in Rockland where you laugh at this invisible humor
This may not be such a serious and depressing poem after all. The speaker admits that he is aiming for "invisible humor," and he imagines that Solomon is laughing along with him.
Why "invisible"? Maybe because Solomon can't actually read the poem because he's on the other side of the country. The poem is not concerned with the "real" Solomon so much as with the speaker's imagined idea of him.
I'm with you in Rockland where we are great writers on the same dreadful typewriter
Ginsberg and Carl Solomon were both writers, so here the speaker essentially shares the credit for this poem with Solomon. As the poem was written, Solomon was there in spirit, as they say.
I'm with you in Rockland where your condition has become serious and is reported on the radio
Solomon is not doing well. He's doing so poorly, in fact, that the news of his condition has reached the radio.
We'd guess that this didn't actually happen, and that the speaker is being ironic. The media usually doesn't place much attention on patients in psychiatric hospitals.