The honeycomb model and regular rigid honeycombs
Allen Knutson
Brandeis University
October 9,
4:15pm
refreshments at 3:45pm
2338
ABSTRACT

We introduce the {\em honeycomb} model of BerensteinZelevinsky polytopes.
This associates a polytope of honeycombs to each triple of dominant weights
of $GL_n$. The BZ theorem says that the lattice points in these polytopes
count LittlewoodRichardson numbers.
Our main result is that for each regular triple of dominant weights,
at least one vertex of this polytope is a particularly nice honeycomb.
One corollary of this is Klyachko's saturation conjecture, which says
that the semigroup of ({\em not} necessarily regular) triples with
$LR>1$ is saturated  the nice honeycombs are necessarily integral.
In this talk we hope to get to another corollary, a description
of those triples of regular dominant weights for which the
LittlewoodRichardson coefficient is exactly 1.
This work is joint with Terry Tao of UCLA.

Speaker's Contact Info: aknaton(atsign)math.mit.edu
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