I just looked at the original confirmation letter I received from AS when I booked my most recent trip. Under the heading marked ITINERARY, it lists each of my flights, and next to the seat assignment, it has the fare class (in my instance, T class). T translates to Hot Deals.

If it was not booked through the AS website (e.g. through a corporate travel office) or you were not sent the intial confirmation, you may not have this.

If you load up the reservation on the AS website, though, there should be a button to view the fare rules. Unfortunately, the last few times I've tried this, it errored out and wouldn't give me the fare rules. (The title of the fare rule should contain a letter for the fare class.)

Even if you could find the fare class letter, we'd be missing one key component: what that translates to according to the AS website. According to SeatCounter.com, here are the inventory codes AS uses (not entirely sure if these match the fare codes):

G L K T S V Q H U M B Y F

Perhaps someone could post here a list of which codes go to which type of fare sold on alaskaair.com...