Séminaire LaCIM: «The dual fans of Demazure polytopes»
Conférencière: Kathlyn Dykes, Carleton University
A Demazure polytope is the convex hull of the weight spaces of aDemazure module. The dual fan of a polytope is a useful tool to study the structure of a polytope. For example, the maximal cones of the can correspond to vertices, while the defining rays of the maximal cones correspond to the codimension 1 hyperplanes of the polytope. By the work of Besson, Jeralds, and Kiers, Demazure polytopes are extremal MV polytopes. The dual fan of an MV polytope was proved byKamnitzer to be a coarsening of a standard fan known as the Weyl fan. Using an appropriate subclass of MV polytopes called MV polytopes of highest vertex w, we will discuss the problem of describing these dual fans from the coarsening of the Weyl fan.
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