Standard Monomials for Positroid Varieties

Ayah Almousa; Shiliang Gao; Daoji Huang

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arXiv · 2309.15384

Standard Monomials for Positroid Varieties

Ayah Almousa·Shiliang Gao·Daoji Huang

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Abstract

We give an explicit characterization of the standard monomials for positroid varieties with respect to the Hodge degeneration and give a Gr\"obner basis. Furthermore, we show that promotion and evacuation biject standard monomials of a positroid variety with those of its cyclic shifts and $w_0$-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.

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Ayah Almousa, Shiliang Gao, Daoji Huang. 2023-09-27. Standard Monomials for Positroid Varieties. https://arxiv.org/abs/2309.15384

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