Comparing Codimension and Absolute Length in Complex Reflection Groups

DOI10.1080/00927872.2013.810748zbMath1314.05229arXiv1202.0266OpenAlexW2962761014MaRDI QIDQ2876292

Briana Foster-Greenwood

Publication date: 18 August 2014

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

Full work available at URL: https://arxiv.org/abs/1202.0266

zbMATH Keywords

Hochschild cohomologyCoxeter groupscodimensionreflection groupspartial ordersreflection length

Mathematics Subject Classification ID

Partial orders, general (06A06) (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items (7)

Drinfeld Hecke algebras for symmetric groups in positive characteristic ⋮ On the Sperner property for the absolute order on complex reflection groups ⋮ Hurwitz numbers for reflection groups. II: Parabolic quasi-Coxeter elements ⋮ Spectra of Cayley graphs of complex reflection groups ⋮ The Hurwitz action in complex reflection groups ⋮ Factorization problems in complex reflection groups ⋮ A note on the Hurwitz action on reflection factorizations of Coxeter elements in complex reflection groups

Uses Software

• GAP
• CHEVIE

Cites Work

• Finite groups acting linearly: Hochschild cohomology and the cup product.
• Cyclic sieving of noncrossing partitions for complex reflection groups.
• Degenerate affine Hecke algebras and Yangians
• Orbifold cohomology for global quotients
• Classification of graded Hecke algebras for complex reflection groups.
• On the quotient ring by diagonal invariants.
• Algebra structure on the Hochschild cohomology of the ring of invariants of a Weyl algebra under a finite group
• Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism.
• Drinfeld orbifold algebras.
• Hochschild duality, localization, and smash products.
• Poisson deformations of symplectic quotient singularities
• Hochschild cohomology on Hopf Galois extensions
• CHEVIE -- A system for computing and processing generic character tables
• Formula for the reflection length of elements in the group \(G(m,p,n)\).
• A PARTIAL ORDER ON THE ORTHOGONAL GROUP
• Non-crossing partition lattices in finite real reflection groups
• Finite Unitary Reflection Groups
• A partial order on the symmetric group and new \(K(\pi,1)\)'s for the braid groups

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