Representation Stability of the Cohomology of Springer Varieties and Some Combinatorial Consequences
Document Type
Article
Publication Date
5-1-2021
Publication Title
Journal of Algebraic Combinatorics
Abstract
A sequence of Sn-representations { Vn} is said to be uniformly representation stable if the decomposition of Vn= ⨁ μcμ,nV(μ) n into irreducible representations is independent of n for each μ—that is, the multiplicities cμ,n are eventually independent of n for each μ. Church–Ellenberg–Farb proved that the cohomology of flag varieties (the so-called diagonal coinvariant algebra) is uniformly representation stable. We generalize their result from flag varieties to all Springer fibers. More precisely, we show that for any increasing subsequence of Young diagrams, the corresponding sequence of Springer representations form a graded co-FI-module of finite type (in the sense of Church–Ellenberg–Farb). We also explore some combinatorial consequences of this stability.
Keywords
Combinatorics, Representation stability, Springer varieties
Volume
53
Issue
3
First Page
897
Last Page
920
DOI
10.1007/s10801-020-00947-2
ISSN
09259899
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.
Recommended Citation
Mbirika, Aba and Tymoczko, Julianna, "Representation Stability of the Cohomology of Springer Varieties and Some Combinatorial Consequences" (2021). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/97
Comments
Peer reviewed accepted manuscript.