Filtering cohomology of ordinary and Lagrangian Grassmannians

This paper studies, 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...

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Published in:arXiv.org 2021-09
Main Authors: The 2020 Polymath Jr REU "q-binomials, the Grassmannian group", Ahmed, Huda, Chishti, Rasiel, Yu-Cheng, Chiu, Dorpalen-Barry, Galen, Ellis, Jeremy, Fang, David, Feigen, Michael, Feigert, Jonathan, González, Mabel, Harker, Dylan, Wei, Jiaye, Joshi, Bhavna, Kulkarni, Gandhar, Lad, Kapil, Liu, Zhen, Ma Mingyang, Myers, Lance, Nigam, Arjun, Popescu, Tudor, Reiner, Victor, Rong, Zijian, Sukarto, Eunice, Leonardo Mendez Villamil, Wang, Chuanyi, Wang, Napoleon, Yamin, Ajmain, Yu, Jeffery, Yu, Matthew, Zhang, Yuanning, Zhu, Ziye, Chen, Zijian
Format: Article
Language:English
Subjects:
Conjugation
Homology
Online Access:Get full text
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Summary:This paper studies, 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.
ISSN:2331-8422
DOI:10.48550/arxiv.2011.03179