Current browse context:
math.AG
Change to browse by:
References & Citations
Mathematics > Algebraic Geometry
Title: A Gröbner basis for Kazhdan-Lusztig ideals of the flag variety of affine type A
(Submitted on 18 Nov 2019 (v1), last revised 25 Apr 2024 (this version, v4))
Abstract: 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 Gr\"obner basis for the Kazhdan-Lusztig ideals. Our result generalizes a result of Woo-Yong that gave a Gr\"obner basis for Kazhdan-Lusztig ideals in the type A flag variety.
Submission history
From: Daoji Huang [view email][v1] Mon, 18 Nov 2019 16:46:50 GMT (63kb,D)
[v2] Tue, 19 Nov 2019 21:15:21 GMT (63kb,D)
[v3] Sun, 27 Nov 2022 22:27:06 GMT (23kb)
[v4] Thu, 25 Apr 2024 17:17:12 GMT (31kb)
Link back to: arXiv, form interface, contact.