A generalization of the saturation theoremAlgebra & Discrete Mathematics
|Speaker:||Michael Kapovich, UC Davis|
|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.