The stone statues of the abstract Union Soldier grow slimmer and younger each year—
Maybe not. This description is more in line with the "sparse" and "frayed" descriptors we read a couple of lines back. Now Lowell describes Colonel Shaw as an "abstract Union Soldier." Abstract means existing in thought or idea, but not in physical presence. Does no one even remember who Colonel Shaw was? Is he simply considered an idea, not a real, human representation of what the Union soldiers fought for?
It's not really possible for the statues to actually "grow slimmer." (Unless you're counting the wind and rain erosion that's wearing them down eensy bit by bit.) This statue in particular is cast of bronze, and can't really change that much. Still, as the speaker ages, wouldn't this statue start to look younger and younger? Think about it.
Of course, these lines likely also have a figurative meaning. If the statues are figuratively getting slimmer and younger, what could that mean? Perhaps that they're fading in people's memories, and that what they fought for is fading as well.
wasp-waisted, they doze over muskets and muse through their sideburns…
"Wasp-waisted" just means skinny. Wasps have really thin abdomens, if you think about it. Ever seen a fat wasp? If you have, email us a pic.
So these skinny little guys doze over their weapons, and think ("muse") through their sideburns. Thinking through their sideburns, huh? That's a strange way to describe it, but if that's how the speaker imagines it, we'll roll with it.
Instead of the speaker looking at the statue of these soldiers and thinking of their physical strength, he pictures them right now as sort of weary philosophers.
The ellipsis (the dot, dot, dot) at the end of the stanza is interesting. Grammatically, that's supposed to indicate a lapse in time. Maybe this is a clue that Lowell is about to jump around again, or maybe he's letting a thought trail off… like a dozing, musing soldier.