\(\mathrm{FI}_{\mathcal{W}}\)-modules and constraints on classical Weyl group characters

DOI10.1007/s00209-015-1473-0zbMath1367.20010arXiv1503.08510OpenAlexW2215805880MaRDI QIDQ495569

Jennifer C. H. Wilson

Publication date: 14 September 2015

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.08510

zbMATH Keywords

characters of sequences of representationsclassical Weyl groupsfinitely generated \(\mathrm{FI}_{\mathcal {W}}\)-module

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Ordinary representations and characters (20C15) Representations of finite symmetric groups (20C30) Cohomology of groups (20J06) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Homology with local coefficients, equivariant cohomology (55N25)

Related Items

Combinatorics of orbit configuration spaces, Asymptotic behavior of representations of graded categories with inductive functors, Representation stability for families of linear subspace arrangements, Topology of arrangements and representation stability. Abstracts from the workshop held January 14--20, 2018, Convergence criteria for \(\text{FI}_{\mathcal{W}}\)-algebras and polynomial statistics on maximal tori in type B/C, Representation stability for the cohomology of arrangements associated to root systems, Representation stability for the pure cactus group, FI-modules and stability for representations of symmetric groups

Cites Work

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• Representation stability for the cohomology of the pure string motion groups.
• FI-modules over Noetherian rings.
• Stabilization for mapping class groups of 3-manifolds
• An inductive approach to Coxeter arrangements and Solomon's descent algebra.
• \(\mathrm{FI}_{\mathcal W}\)-modules and stability criteria for representations of classical Weyl groups.
• Die Charaktere der symmetrischen Gruppe
• Groups and Lie algebras corresponding to the Yang-Baxter equations
• Automorphisms of two-dimensional RAAGS and partially symmetric automorphisms of free groups.
• On the action of the symmetric group on the cohomology of the complement of its reflecting hyperplanes
• Combinatorics and topology of complements of hyperplanes
• The theory of motion groups
• On the cohomology of an arrangement of type \(B_ l\)
• The cohomology ring of the colored braid group
• Dold-Kan type theorem for \(\Gamma\)-groups
• Virtual knot theory
• Automorphisms of free groups with boundaries.
• Homological stability for automorphism groups of free groups
• Configuration spaces of rings and wickets
• Character polynomials, their \(q\)-analogs and the Kronecker product.
• Stable decompositions for some symmetric group characters arising in braid group cohomology.
• Representation theory and homological stability.
• A combinatorial proof of the degree theorem in Auter space.
• Rational homological stability for groups of partially symmetric automorphisms of free groups.
• The integral cohomology of the group of loops.
• Finiteness properties of automorphism groups of right-angled Artin groups
• On Basis-Conjugating Automorphisms of Free Groups
• Hodge decomposition for higher order Hochschild homology
• ON HOMOLOGY OF VIRTUAL BRAIDS AND BURAU REPRESENTATION
• The virtual and universal braids
• Virtual braids
• Symmetric automorphisms of free products
• Diagonal complexes and the integral homology of the automorphism group of a free product
• HOMOLOGICAL STABILITY FOR UNLINKED CIRCLES IN A 3-MANIFOLD
• Stabilité Homologique pour les Groupes d’automorphismes des Produits Libres
• PROPER ACTIONS OF AUTOMORPHISM GROUPS OF FREE PRODUCTS OF FINITE GROUPS
• The Characters of the Symmetric Group
• The Analysis of the Kronecker Product of Irreducible Representations of the Symmetric Group
• The Characters of the Symmetric Group