Subword complexes via triangulations of root polytopes

Escobar, Laura; Mészáros, Karola

Algebraic Combinatorics, Tome 1 (2018) no. 3, pp. 395-414.

Subword complexes are simplicial complexes introduced by Knutson and Miller to illustrate the combinatorics of Schubert polynomials and determinantal ideals. They proved that any subword complex is homeomorphic to a ball or a sphere and asked about their geometric realizations. We show that a family of subword complexes can be realized geometrically via regular triangulations of root polytopes. This implies that a family of $\beta$-Grothendieck polynomials are special cases of reduced forms in the subdivision algebra of root polytopes. We can also write the volume and Ehrhart series of root polytopes in terms of $\beta$-Grothendieck polynomials.

Classification : 52B20, 05E45
Mots-clés : subword complex, pipedream, triangulation, root polytope

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