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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 |
Description
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.