Upper bounds of dual flagged Weyl characters

• Published in: Advances in applied mathematics Vol. 160; p. 102752
• Main Authors: Peng, Simon C.Y., Lin, Zhuowei, Sun, Sophie C.C.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-09-2024
• Subjects: Dual character; Flagged Weyl module; Upper bound; 05E05; Flagged Weyl module; Upper bound; 14N15; Dual character
• ISSN: 0196-8858
• DOI: 10.1016/j.aam.2024.102752

For a subset D of boxes in an n×n square grid, let χD(x) denote the dual character of the flagged Weyl module associated to D. It is known that χD(x) specifies to a Schubert polynomial (resp., a key polynomial) in the case when D is the Rothe diagram of a permutation (resp., the skyline diagram of a composition). One can naturally define a lower and an upper bound of χD(x). Mészáros, St. Dizier and Tanjaya conjectured that χD(x) attains the upper bound if and only if D avoids a certain single subdiagram. We provide a proof of this conjecture.