Schubert calculus and the Hopf algebra structures of exceptional Lie groups

DOI10.1515/form.2011.154zbMath1320.14063arXiv0903.4501OpenAlexW2963969822WikidataQ115236452 ScholiaQ115236452MaRDI QIDQ3189487

Xuezhi Zhao, Hai Bao Duan

Publication date: 11 September 2014

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.4501

zbMATH Keywords

Schubert calculusLie groupsHopf algebraSteenrod algebra

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Homology and cohomology of homogeneous spaces of Lie groups (57T15) Classical problems, Schubert calculus (14N15) Hopf algebras and their applications (16T05)

Related Items (4)

Computation of the cohomology rings of Kac-Moody groups, their flag manifolds and classifying spaces ⋮ On the number of simplices required to triangulate a Lie group ⋮ Schubert presentation of the cohomology ring of flag manifolds ⋮ On Schubert’s Problem of Characteristics

Cites Work

• The Chow rings of generalized Grassmannians
• The integral cohomology ring of \(E_{8}/T\)
• Torsion in cohomology of compact Lie groups and Chow rings of reductive algebraic groups
• Cohomology mod 2 of the classifying space of the compact connected Lie group of type E\(_8\)
• On the cohomology mod 2 of the classifying space of the 1-connected exceptional Lie group \(E_7\)
• Hopf algebra structure of mod 2 cohomology of simple Lie groups
• On the inverse Kostka matrix
• Exceptional Lie groups and Steenrod squares
• Invariants symétriques entiers des groupes de Weyl et torsion
• Characteristic Classes and Homogeneous Spaces, I
• Cohomology Operations and the Hopf Algebra Structures of the Compact, Exceptional Lie Groups E ₇ and E ₈
• A combinatorial interpretation of the inverse kostka matrix
• Cohomology Mod $2$ of the compact exceptional group $E_8$
• On the Non-Commutativity of Pontrjagin Rings Mod 3 of Some Compact Exceptional Groups
• The Iteration of the Steenrod Squares in Algebraic Topology
• Sur L'Homologie et la Cohomologie des Groupes de Lie Compacts Connexes

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