Affine Grassmannians And Hessenberg Schubert Cells
Document Type
Book Chapter
Publication Date
2019
Published In
Recent Trends In Algebraic Combinatorics
Series Title
Association For Women In Mathematics
Abstract
We give an overview of the linear algebra, geometry, and combinatorics of affine Grassmannians along the lines of Fulton’s Young Tableaux for classical Grassmannians. We discuss geometric and linear algebraic aspects of the decomposition of the affine Grassmannian into affine Schubert cells in terms of coset representatives and linear models. We describe (Grassmannian) Hessenberg Schubert cells and show that every affine Schubert cell can be realized as a Hessenberg Schubert cell in a complete flag variety and as a Grassmannian Hessenberg Schubert cell in a finite Grassmannian.
Published By
Springer
Editor(s)
H. Barcelo, G. Karaali, and R. Orellana
Recommended Citation
Linda Chen and J. Tymoczko.
(2019).
"Affine Grassmannians And Hessenberg Schubert Cells".
Recent Trends In Algebraic Combinatorics.
Volume 16,
43-74.
DOI: 10.1007/978-3-030-05141-9_2
https://works.swarthmore.edu/fac-math-stat/246