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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1911.07760 |
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| _version_ | 1866911851854430208 |
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| author | Elek, Balázs Huang, Daoji |
| author_facet | Elek, Balázs Huang, Daoji |
| contents | A Kazhdan-Lusztig variety is the intersection of a locally-closed Schubert cell with an opposite Schubert variety in a flag variety. We present a linear parametrization of the Schubert cells in the affine type A flag variety via Bott-Samelson maps, and give explicit equations that generate the Kazhdan-Lusztig ideals in these coordinates. Furthermore, our equations form a Gröbner basis for the Kazhdan-Lusztig ideals. Our result generalizes a result of Woo-Yong that gave a Gröbner basis for Kazhdan-Lusztig ideals in the type A flag variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_07760 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A Gröbner basis for Kazhdan-Lusztig ideals of the flag variety of affine type A Elek, Balázs Huang, Daoji Algebraic Geometry Combinatorics 14M15 A Kazhdan-Lusztig variety is the intersection of a locally-closed Schubert cell with an opposite Schubert variety in a flag variety. We present a linear parametrization of the Schubert cells in the affine type A flag variety via Bott-Samelson maps, and give explicit equations that generate the Kazhdan-Lusztig ideals in these coordinates. Furthermore, our equations form a Gröbner basis for the Kazhdan-Lusztig ideals. Our result generalizes a result of Woo-Yong that gave a Gröbner basis for Kazhdan-Lusztig ideals in the type A flag variety. |
| title | A Gröbner basis for Kazhdan-Lusztig ideals of the flag variety of affine type A |
| topic | Algebraic Geometry Combinatorics 14M15 |
| url | https://arxiv.org/abs/1911.07760 |