Return to Colloquia & Seminar listing

### A generalization of the saturation theorem

**Algebra & Discrete Mathematics**

Speaker: | Michael Kapovich, UC Davis |

Location: | 693 Kerr |

Start time: | Fri, Dec 10 2004, 12:10PM |

In 1999 Knutson and Tao proved the following "saturation conjecture":

Consider the semigroup $S$ of triples $(a,b,c)$ of dominant weights of $GL(n,C)$ such that the tensor product of the irreducible representations $V_a$, $V_b$ and $V_c$ of $GL(n,C)$ contains trivial repesentation. Then $S$ is "saturated", i.e. a triple of dominant weights $s=(a,b,c)$ belongs to $S$ if and only if there exists a natural number $N$ such that $Ns$ belongs to $S$.

In this talk I will explain how to generalize this result to other reductive complex Lie groups and how it relates to the geometry of Euclidean building. Along the way I will describe a generalization of Littelmann's path model to Hecke rings. This is a joint work with John Millson.