Standard Monomials for Positroid Varieties
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911736869683200 |
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| author | Almousa, Ayah Gao, Shiliang Huang, Daoji |
| author_facet | Almousa, Ayah Gao, Shiliang Huang, Daoji |
| contents | 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 $w_0$-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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_15384 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Standard Monomials for Positroid Varieties Almousa, Ayah Gao, Shiliang Huang, Daoji Algebraic Geometry Commutative Algebra Combinatorics 14M15, 05E14, 05E40, 13P10, 05E10 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 $w_0$-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. |
| title | Standard Monomials for Positroid Varieties |
| topic | Algebraic Geometry Commutative Algebra Combinatorics 14M15, 05E14, 05E40, 13P10, 05E10 |
| url | https://arxiv.org/abs/2309.15384 |