Abstract: Demazure modules are certain $B$-submodules of irreducible G-modules, where $B$ is a Borel subgroup of a semisimple Lie group $G$.
They arise as cohomology groups of line bundles on Schubert
varieties, and their characters enjoy several nice properties, including a generalization of the Weyl character formula.
We will consider the weight polytopes associated to these
characters, presenting basic formulas and results on them.
We will show how the polytopes shed light on the supports
of the characters, at least in classical types. This gives
an alternate proof of a conjecture of Monical, Tokcan, and
Yong, first proven by Fink, Mészáros, and St. Dizier. |