Affine Grassmannians and Hessenberg Schubert Cells

Authors

Linda Chen, Swarthmore College
Julianna Tymoczko, Smith CollegeFollow

Document Type

Book Chapter

Publication Date

2019

Publication Title

Recent trends in Algebraic Combinatorics

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.

Volume

16

First Page

50

Last Page

74

DOI

doi.org/10.1007/978-3-030-05141-9_2

Recommended Citation

Chen, Linda and Tymoczko, Julianna, "Affine Grassmannians and Hessenberg Schubert Cells" (2019). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/51