Dynkin diagram classification of \(\lambda\)-minuscule Bruhat lattices and of \(d\)-complete posets

DOI10.1023/A:1018615115006zbMath0920.06003OpenAlexW371866709MaRDI QIDQ1283505

Robert A. Proctor

Publication date: 16 May 1999

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1018615115006

zbMATH Keywords

Coxeter groupsBruhat orderDynkin diagramsalgebraic geometryplane partitionsLie theoryalgebraic combinatoricsreduced decomposition\(d\)-complete posets\(\lambda\)-minuscule elements\(\lambda\)-minuscule Schubert varietiesBruhat distributive latticeshook length posetsminuscule Weyl group elementshifted shapessimply laced Weyl group

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Combinatorics of partially ordered sets (06A07) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

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Cites Work

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• A Dynkin diagram classification theorem arising from a combinatorial problem
• Enumeration of partitions with hooklengths
• Minuscule elements of Weyl groups, the numbers game, and \(d\)-complete posets
• Reflection processes on graphs and Weyl groups
• On the fully commutative elements of Coxeter groups
• Bruhat lattices, plane partition generating functions, and minuscule representations
• Reflection Sequences
• Ordered structures and partitions

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