Affine Grassmannians and Hessenberg Schubert Cells

  • Linda ChenEmail author
  • Julianna Tymoczko
Part of the Association for Women in Mathematics Series book series (AWMS, volume 16)


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.


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Copyright information

© The Author(s) and the Association for Women in Mathematics 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsSwarthmore CollegeSwarthmoreUSA
  2. 2.Department of Mathematics and StatisticsSmith CollegeNorthamptonUSA

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