On two presentations of the affine Weyl groups of classical types

DOI10.1006/jabr.1999.8000zbMath0946.20019OpenAlexW2091779763MaRDI QIDQ1818842

Jian-yi Shi

Publication date: 3 August 2000

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

Full work available at URL: https://doi.org/10.1006/jabr.1999.8000

zbMATH Keywords

presentationsaffine Weyl groupsCoxeter systemsalcovesinverse tables

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Other geometric groups, including crystallographic groups (20H15)

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The \(\widehat W\)-orbit of \(\rho\), Kostant's formula for powers of the Euler product and affine Weyl groups as permutations of \(\mathbb Z\)., Abacus models for parabolic quotients of affine Weyl groups, A description of the minimal elements of Shi regions in classical Weyl groups, The second lowest two-sided cell in the affine Weyl group \(\widetilde{B}_n\), The second lowest two-sided cell in an affine Weyl group., Bijections between generalized Catalan families of types \(A\) and \(C\), Results and conjectures on simultaneous core partitions, An order on circular permutations, 𝑎𝑑-nilpotent 𝔟-ideals in 𝔰𝔩(𝔫) having a fixed class of nilpotence: combinatorics and enumeration

Cites Work

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• Infinite dimensional Lie algebras. An introduction
• The Kazhdan-Lusztig cells in certain affine Weyl groups
• The generalized Robinson-Schensted algorithm on the affine Weyl group of type \(A_{n-1}\)
• Some results relating two presentations of certain affine Weyl groups
• Affine Weyl groups as infinite permutations
• On some Bruhat decomposition and the structure of the Hecke rings of \(p\)-adic Chevalley groups
• Some Examples of Square Integrable Representations of Semisimple p-Adic Groups
• Cells for two coxeter groups
• Alcoves Corresponding to an Affine Weyl Group