Filtering cohomology of ordinary and Lagrangian Grassmannians

Reiner, Victor; Dorpalen-Barry, Galen

doi:10.2140/involve.2022.15.271

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-4184 (online)

ISSN 1944-4176 (print)

Author index

To appear

Other MSP journals

Filtering cohomology of ordinary and Lagrangian Grassmannians

Victor Reiner and Galen Dorpalen-Barry

Vol. 15 (2022), No. 2, 271–288

DOI: 10.2140/involve.2022.15.271

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.

Keywords

Grassmannian, Lagrangian, Hilbert series, $q$-binomial, $k$-conjugation, $k$-Schur function

Mathematical Subject Classification

Primary: 05E05, 05E14, 14N15

Milestones

Received: 21 March 2021

Revised: 10 September 2021

Accepted: 11 September 2021

Published: 29 July 2022

Communicated by Jim Haglund

Authors

Victor Reiner
School of Mathematics University of Minnesota Minneapolis, MN United States

Galen Dorpalen-Barry
Fakultät für Mathematik Ruhr-Universität Bochum Bochum Germany

Vol. 15, No. 2, 2022