Filtering cohomology of ordinary and Lagrangian Grassmannians The 2020 Polymath Jr. “q-binomials and the Grassmannian” group

Victor Reiner, Galen Dorpalen-Barry

Research output: Contribution to journalArticlepeer-review

Abstract

We study, for a positive integer m, the subalgebra of the cohomology ring of the complex Grassmannians generated by the elements of degree at most m. We build in two ways upon a conjecture for the Hilbert series of this subalgebra due to Reiner and Tudose. The first reinterprets it in terms of the operation of k-conjugation, suggesting two conjectural bases for the subalgebras that would imply their conjecture. The second introduces an analogous conjecture for the cohomology of Lagrangian Grassmannians.

Original languageEnglish (US)
Pages (from-to)271-288
Number of pages18
JournalInvolve
Volume15
Issue number2
DOIs
StatePublished - 2022

Bibliographical note

Funding Information:
The work of Reiner and Dorpalen-Barry was supported by NSF grant DMS-1601961. The team also sincerely thanks the Polymath Jr. REU faculty organizers (Kira Adaricheva, Ben Brubaker, Pat Devlin, Steven Miller, Alexandra Seceleanu, Adam Sheffer, Yunus Zeytuncu) for their vision and hard work in making this bold new opportunity a reality. We also acknowledge the work of participant Huda Ahmed.

Publisher Copyright:
© 2022, Mathematical Sciences Publishers. All rights reserved.

Keywords

  • Grassmannian
  • Hilbert series
  • k-conjugation
  • k-Schur function
  • Lagrangian
  • q-binomial

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