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MIT Combinatorics Seminar

The glue between Young tableaux

Allen Knutson  (UC Berkeley)
http://math.berkeley.edu/~allenk/

Friday, October 15, 2004    4:15 pm    Room 2-338

ABSTRACT

Young tableaux, beloved of combinatorialists, tolerated by representation theorists and geometers, seem at first glance to be an unruly combinatorial set. I'll define a simplicial complex in which they index the facets, and slightly more general objects (Buch's ``set-valued tableaux'') label the other interior faces.

The theorem that says we're on a right track: This simplicial complex is homeomorphic to a ball. I'll explain why this is surprising, useful, and shows why Buch didn't discover the exterior faces too.

Finally, I'll explain how algebraic geometry forced these definitions on us (or, ``How I made my peace with Young tableaux''). This work is joint with Ezra Miller and Alex Yong.