Views of Castalia
by Arun Ram
Abstract: There are three mountains (the preprojective variety, the quiver variety and the loop Grassmannian).
These three mountains feed the spring at their base (the quantum group). At the spring
live three nymphs, very similar, but different (the semicanonical basis,
the canonical basis and the MV basis). Each of these is nourished by
the special nutrients of the corresponding source (the preprojective variety,
the quiver variety and the loop Grassmannian).
At three particular moments of each day (dawn, noon, dusk) the shadow of the
muses on the valley below is the same (the MV polytope).
And, as we shall see, there is a Glass Bead Game in this story as well.