Standard monomials for positroid varieties

Authors

• Ayah Almousa, University of KentuckyFollow
• Shiliang Gao, Cornell University
• Daoji Huang, University of MassachusettsFollow

Abstract

We give an explicit characterization of the standard monomials for positroid varieties with respect to the Hodge degeneration and give a Gröbner basis. Furthermore, we show that promotion and evacuation biject standard monomials of a positroid variety with those of its cyclic shifts and w₀-reflection, respectively. The connection to promotion allows us to identify standard monomials of a positroid variety with Lam's cyclic Demazure crystal. Using a recurrence on the Hilbert series, we give an inductive formula for the character of cyclic Demazure modules.

Document Type

Article

Publication Date

9-1-2026

Notes/Citation Information

Publisher Copyright: Copyright © 2026. Published by Elsevier Inc.

Digital Object Identifier (DOI)

10.1016/j.aim.2026.111090

Archival?

Archival

Repository Citation

Almousa, Ayah; Gao, Shiliang; and Huang, Daoji, "Standard monomials for positroid varieties" (2026). Mathematics Faculty Publications. 52.
https://uknowledge.uky.edu/math_facpub/52