Consider a root system $R$ and the corresponding toric variety $V_R$ whose fan is the Weyl fan and whose lattice of characters is given by the root lattice for $R$. We prove the vanishing of the higher cohomology groups for certain line bundles on $V_R$ by proving a purely combinatorial result for root systems. These results are related to a converse to Mazur's Inequality for (simply-connected) split reductive groups.
Stability conditions for preprojective algebras and root systems of Kac-Moody Lie algebras
Projection of root systems
Klein operator and the Numbers of independent Traces and Supertraces on the Superalgebra of Observables of Rational Calogero Model based on the Root System
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