Ehrhart positivity and Demazure characters

@article{Alexandersson2019EhrhartPA,
  title={Ehrhart positivity and Demazure characters},
  author={Per Alexandersson and Elie Alhajjar},
  journal={Algebraic and Geometric Combinatorics on Lattice Polytopes},
  year={2019}
}
Demazure characters, also known as key polynomials, generalize the classical Schur polynomials. In particular, when all variables are set equal to $1$, these polynomials count the number of integer points in a certain class of Gelfand--Tsetlin polytopes. This property highlights the interaction between the corresponding polyhedral and combinatorial structures via Ehrhart theory. In this paper, we give an overview of results concerning the interplay between the geometry of Gelfand-Tsetlin… 

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