Slide polynomials and subword complexes
Sbornik. Mathematics, Tome 212 (2021) no. 10, pp. 1471-1490
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Subword complexes were defined by Knutson and Miller in 2004 to describe Gröbner degenerations of matrix Schubert varieties. Subword complexes of a certain type are called pipe dream complexes. The facets of such a complex are indexed by pipe dreams, or, equivalently, by monomials in the corresponding Schubert polynomial. In 2017 Assaf and Searles defined a basis of slide polynomials, generalizing Stanley symmetric functions, and described a combinatorial rule for expanding Schubert polynomials in this basis. We describe a decomposition of subword complexes into strata called slide complexes. The slide complexes appearing in such a way are shown to be homeomorphic to balls or spheres. For pipe dream complexes, such strata correspond to slide polynomials.
Bibliography: 14 titles.
Keywords:
flag varieties, Schubert polynomials, Grothendieck polynomials, simplicial complexes.
@article{SM_2021_212_10_a4,
author = {E. Yu. Smirnov and A. A. Tutubalina},
title = {Slide polynomials and subword complexes},
journal = {Sbornik. Mathematics},
pages = {1471--1490},
publisher = {mathdoc},
volume = {212},
number = {10},
year = {2021},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2021_212_10_a4/}
}
E. Yu. Smirnov; A. A. Tutubalina. Slide polynomials and subword complexes. Sbornik. Mathematics, Tome 212 (2021) no. 10, pp. 1471-1490. http://geodesic.mathdoc.fr/item/SM_2021_212_10_a4/