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Filtering
cohomology of ordinary and Lagrangian Grassmannians
Victor Reiner and Galen Dorpalen-Barry
Vol. 15 (2022), No. 2, 271–288
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Abstract |
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We study, 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. |
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Keywords
Grassmannian, Lagrangian, Hilbert series, $q$-binomial,
$k$-conjugation, $k$-Schur function
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Mathematical Subject Classification
Primary: 05E05, 05E14, 14N15
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Milestones
Received: 21 March 2021
Revised: 10 September 2021
Accepted: 11 September 2021
Published: 29 July 2022
Communicated by Jim Haglund
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Authors |
| Victor Reiner | |
| School of Mathematics University of Minnesota Minneapolis, MN United States |
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| Galen Dorpalen-Barry | |
| Fakultät für Mathematik Ruhr-Universität Bochum Bochum Germany |
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