Gr\'obner geometry of Schubert polynomials through ice

Autor:	Zachary Hamaker, Oliver Pechenik, Anna Weigandt
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	Mathematics - Algebraic Geometry General Mathematics Mathematics - Combinatorics 05E40 14M12 Mathematics - Commutative Algebra
Popis:	The geometric naturality of Schubert polynomials and their combinatorial pipe dream representations was established by Knutson and Miller (2005) via antidiagonal Gr\"obner degeneration of matrix Schubert varieties. We consider instead diagonal Gr\"obner degenerations. In this dual setting, Knutson, Miller, and Yong (2009) obtained alternative combinatorics for the class of "vexillary'' matrix Schubert varieties. We initiate a study of general diagonal degenerations, relating them to a neglected formula of Lascoux (2002) in terms of the $6$-vertex ice model (recently rediscovered by Lam, Lee, and Shimozono (2018) in the guise of "bumpless pipe dreams''). Comment: 22 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::09229f557ba3c697c2d24aa1e8993303 http://arxiv.org/abs/2003.13719 Zobrazit plný text záznamu