OK, I'm back...
Well, this hing with the alvar is a bit tricky, especially for those who grow up outside of the Scandinavian culture, because you really only have the two Eddas to go by. Most of the stories about alvar come from the lore, the oral tradition which, for he most part, has not been translated or, when it has, is not commonly read by non-Scandinavians. To make matters worse, the Eddas give us two different accounts of the alvar. According to Snorri, there are ljosalfar, who live "in heaven" and are more beautiful than the sun, and then there are dokkalfar (sorry about the spelling - I'm on the wrong computer and this keyboard lacks the correct symbols...), who live in the ground and are black. Some scholars think that this was somehing Snorri got from Christianity, where there is a good and a bad side to things.
The Poetic Edda, on the other hand, tells of "aesir and alvar", which can be interpreted as "all the gods". In one story, a Christian named Sigvat stops at a farm and requests lodging, but is told that he cannot stay there, since the folk at the farm are holdig a blot to the alfr (alfarblot), and Christians shouldn't be present. That's where the idea that Bates explained about comes in, becasue some then have thought that since the aesir and the vanir are what generally constitutes "all the gods", then alfr might be synonymous to vanir. It's also the reason why the alfr have been associated with fertility, seeing as how the vanir were the fertility gods and goddesses. To boot, Frej, who's the main fertility god, lives in Alfheim. Then there's also the issue of some powerful men who, upon their death, obtain the title of alfr, which has been interpreted as the alfr having to do with ancestor worshipry (again, the idea of a blot held in their honour would fit in with this theory, as the female ancestor spirits, the disir, are honoured with a blot every year).
In the ring of the Nibelungs and/or the Song of Völund the king of the alfr is Völund, who is captured and enslaved but then avenges this fate.
Anyhow, as you see, this Icelandic litterature is contradictory. The folklore is much more clear. In it, the darkalf is called that becasue he is dark in spirit, not just in his looks. He is fickle and tricky to deal with, so you have to make sure to pay him well for what he does for you, or he'll cause all sorts of trouble. He can turns to stone if he is hit by sunlight.
Lightalfs, on the other hand, are bnign and help us out in various ways. They keep us and our livestock safe and healthy.
These beings are some of the ones that Christianity has been completely unable to erase even 1000 years after the conversion. Even when I was brought up, kids were told not to run in the house, make too much noise in the house and to take their shoes off in the house, lest you bother or annoy the alfar who live under the floor. You do not want to do that, since they might leave then, and if they do, there would b nobody left to help keep you and yours safe in he house. Eventually, these beings were sucked p ino he Christian mythology. The Swedish version of Santa is actually an alf, much in the same way as the English Santa has helpers who are - guess what? - the Anglo-Saxon version of alfar!
So, now that you're completely confused, I'll stop.
