Algebra, Geometry & Combinatorics: A Gröbner basis for Kazhdan-Lusztig ideals in the flag variety of affine type A
- Event Type
- Seminar/Symposium
- Sponsor
- N/A
- Location
- 241 AH
- Date
- Nov 10, 2022 3:00 pm
- Speaker
- Daoji Huang
- Contact
- Gidon Orelowitz
- Views
- 35
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. This is joint work with Balázs Elek.