Filtering cohomology of ordinary and Lagrangian Grassmannians
Combinatorics
2022-08-10 v2
Abstract
This paper studies, for a positive integer , the subalgebra of the cohomology ring of the complex Grassmannians generated by the elements of degree at most . 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 -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.
Cite
@article{arxiv.2011.03179,
title = {Filtering cohomology of ordinary and Lagrangian Grassmannians},
author = {The 2020 Polymath Jr. REU "q-binomials and the Grassmannian group" and : and Huda Ahmed and Rasiel Chishti and Yu-Cheng Chiu and Galen Dorpalen-Barry and Jeremy Ellis and David Fang and Michael Feigen and Jonathan Feigert and Mabel González and Dylan Harker and Jiaye Wei and Bhavna Joshi and Gandhar Kulkarni and Kapil Lad and Zhen Liu and Ma Mingyang and Lance Myers and Arjun Nigam and Tudor Popescu and Victor Reiner and Zijian Rong and Eunice Sukarto and Leonardo Mendez Villamil and Chuanyi Wang and Napoleon Wang and Ajmain Yamin and Jeffery Yu and Matthew Yu and Yuanning Zhang and Ziye Zhu and Chen Zijian},
journal= {arXiv preprint arXiv:2011.03179},
year = {2022}
}
Comments
Version to appear in Involve