# Mathematics Colloquia and Seminars

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### Rotation and the Satake fiber

**Geometry/Topology**

Speaker: | Bruce Fontaine, MSRI and Cornell University |

Location: | 2112 MSB |

Start time: | Tue, Nov 6 2012, 3:10PM |

For complex semi-simple group G,a Satake fiber is the set of cyclic configurations of points in the Affine Grassmannian with fixed distances between consecutive points. The irreducible components of this variety are naturally labelled by certain closed dominant (Littelmann) paths in the weight lattice of G and also give rise to a basis of the G-invariant space of a tensor product of G representations. All three things have a natural actions of rotation which are essentially the same. We will show that geometric rotation of components of the Satake fiber becomes a combinatorial rotation on the set of labelling paths and corresponds, up to a determined sign, to rotation of tensor factors.

Joint with the Algebra and Discrete Math seminar.