Resumen de Cyclic sieving, rotation, and geometric representation theory
Bruce Fontaine, Joel Kamnitzer
We study rotation of invariant vectors in tensor products of minuscule representations. We define a combinatorial notion of rotation of minuscule Littelmann paths. Using affine Grassmannians, we show that this rotation action is realized geometrically as rotation of components of the Satake fiber. As a consequence, we have a basis for invariant spaces, which is permuted by rotation (up to global sign). Finally, we diagonalize the rotation operator by showing that its eigenspaces are given by intersection homology of quiver varieties. As a consequence, we generalize Rhoades’ work on the cyclic sieving phenomenon.
