Bases for the Bruhat-Chevalley order on all finite Coxeter groups

DOI10.1006/jabr.1997.7096zbMath0977.20033OpenAlexW1986201476MaRDI QIDQ1376340

Sungsoon Kim, Meinolf Geck

Publication date: 21 January 2002

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1997.7096

zbMATH Keywords

algorithmsparabolic subgroupscomputer algebra systemsfinite Coxeter groupspartially ordered setsBruhat-Chevalley ordersright coset representativesbi-Grassmannians

Mathematics Subject Classification ID

Partial orders, general (06A06) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items (12)

Hultman elements for the hyperoctahedral groups ⋮ Left cells in type 𝐵_{𝑛} with unequal parameters ⋮ Diagrams and essential sets for signed permutations ⋮ The maximum number of atoms of Bruhat intervals in the symmetric groups. ⋮ Enumeration of bigrassmannian permutations below a permutation in Bruhat order ⋮ Posets of finite functions ⋮ Recognizing Schubert cells. ⋮ Weighted counting of inversions on alternating sign matrices ⋮ Reflection Groups ⋮ Presenting the cohomology of a Schubert variety ⋮ On comparability of bigrassmannian permutations ⋮ Pipe dreams for Schubert polynomials of the classical groups

Uses Software

• GAP
• CHEVIE

Cites Work

• Classical Bruhat orders and lexicographic shellability
• Some characterizations of Bruhat ordering on a Coxeter group and determination of the relation Möbius function
• CHEVIE -- A system for computing and processing generic character tables
• Characters of Reductive Groups over a Finite Field. (AM-107)
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