Ehrhart positivity and Demazure characters

  title={Ehrhart positivity and Demazure characters},
  author={Per Alexandersson and Elie Alhajjar},
  journal={Algebraic and Geometric Combinatorics on Lattice Polytopes},
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… 

Figures and Tables from this paper


On Decomposition of the Product of Demazure atoms and Demazure Characters
This paper studies the properties of Demazure atoms and characters using linear operators and also tableaux-combinatorics. It proves the atom-positivity property of the product of a dominating
An explicit construction of type A Demazure atoms
Demazure characters of type A, which are equivalent to key polynomials, have been decomposed by Lascoux and Schützenberger into standard bases. We prove that the resulting polynomials, which we call
Schubert Geometry of Flag Varieties and Gelfand-Cetlin Theory
This thesis investigates the connection between the geometry of Schubert varieties and Gelfand-Cetlin coordinates on ag manifolds. In particular, we discovered a connection between Schubert calculus
Schubert calculus and Gelfand-Zetlin polytopes
A new approach is described to the Schubert calculus on complete flag varieties, using the volume polynomial associated with Gelfand-Zetlin polytopes. This approach makes it possible to compute the
Arithmetic of Marked Order Polytopes, Monotone Triangle Reciprocity, and Partial Colorings
The marked order polytope parametrizes the order preserving extensions of F to P and the function counting integral-valued extensions is a piecewise polynomial in F and a reciprocity statement is proved in terms of order-reversing maps.
A combinatorial formula for affine Hall–Littlewood functions via a weighted Brion theorem
We present a new combinatorial formula for Hall–Littlewood functions associated with the affine root system of type $${{\tilde{A}}}_{n-1}$$A~n-1, i.e., corresponding to the affine Lie algebra