Springer Fibers and Schubert Points

Authors

Martha Precup, Washington University in St. Louis
Julianna Tymoczko, Smith CollegeFollow

Document Type

Article

Publication Date

2-2019

Publication Title

European Journal of Combinatorics

Abstract

Springer fibers are subvarieties of the flag variety parametrized by partitions; they are central objects of study in geometric representation theory. Schubert varieties are subvarieties of the flag variety that induce a well-known basis for the cohomology of the flag variety. This paper relates these two varieties combinatorially. We prove that the Betti numbers of the Springer fiber associated to a partition with at most three rows or two columns are equal to the Betti numbers of a specific union of Schubert varieties.

Volume

76

First Page

10

Last Page

26

DOI

doi.org/10.1016/j.ejc.2018.08.010

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Rights

Licensed to Smith College and distributed CC-BY under the Smith College Faculty Open Access Policy.

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Precup, Martha and Tymoczko, Julianna, "Springer Fibers and Schubert Points" (2019). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/52