On minimal lengths of expressions of Coxeter group elements as products of reflections

DOI10.1090/S0002-9939-01-05876-2zbMath0980.20028OpenAlexW1510366593MaRDI QIDQ2716101

Matthew J. Dyer

Publication date: 6 June 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-01-05876-2

zbMATH Keywords

Coxeter groupslengths of wordssimple reflectionsproducts of reflectionsBruhat graphs\(R\)-polynomials

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items (27)

INVERSIONS IN CLASSICAL WEYL GROUPS ⋮ Report on locally finite triangulated categories ⋮ Hultman elements for the hyperoctahedral groups ⋮ THE CANCELLATION NORM AND THE GEOMETRY OF BI-INVARIANT WORD METRICS ⋮ Variations of the Poincaré series for affine Weyl groups and \(q\)-analogues of Chebyshev polynomials ⋮ A categorification of non-crossing partitions ⋮ Depth in classical Coxeter groups ⋮ Shortest path poset of Bruhat intervals ⋮ More on the combinatorial invariance of Kazhdan-Lusztig polynomials ⋮ Interval groups related to finite Coxeter groups. I ⋮ Dual garside structures and Coxeter sortable elements ⋮ Reflection ordering on the group \(G(m,m,n)\). ⋮ Interval groups related to finite Coxeter groups Part II ⋮ A Garside presentation for Artin-Tits groups of type \(\widetilde C_n\). ⋮ Bounding reflection length in an affine Coxeter group. ⋮ The absolute order of a permutation representation of a Coxeter group ⋮ Context adaptation of mamdani fuzzy rule based systems ⋮ An upper bound for reflection length in Coxeter groups ⋮ Exceptional sequences and clusters. (With an appendix with Hugh Thomas). ⋮ Fixed points of involutive automorphisms of the Bruhat order ⋮ Proof of the \(K(\pi,1)\) conjecture for affine Artin groups ⋮ A note on the transitive Hurwitz action on decompositions of parabolic Coxeter elements ⋮ On the Hurwitz action in affine Coxeter groups ⋮ Weak \(Z\)-property of the absolute order on groups generated by sets closed under taking inverses ⋮ First-order aspects of Coxeter groups ⋮ Noncrossing partitions and representations of quivers ⋮ Dimensions of Affine Deligne–Lusztig Varieties: A New Approach via Labeled Folded Alcove Walks and Root Operators

Cites Work

• Reflection subgroups of Coxeter systems
• On some geometric aspects of Bruhat orderings. I: A finer decomposition of Bruhat cells
• Representations of Coxeter groups and Hecke algebras
• A combinatorial formula for Kazhdan-Lusztig polynomials
• Invariants of Finite Reflection Groups
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