Representation theory and homological stability.

DOI10.1016/j.aim.2013.06.016zbMath1300.20051arXiv1008.1368OpenAlexW2037343549MaRDI QIDQ2437478

Benson Farb, Thomas Church

Publication date: 3 March 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.1368

zbMATH Keywords

braid groupsirreducible representationshomological stabilityuniform representation stability

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Braid groups; Artin groups (20F36) Cohomology of groups (20J06) Discriminantal varieties and configuration spaces in algebraic topology (55R80) Cohomology theory for linear algebraic groups (20G10) Stability for linear groups (19B14)

Related Items (98)

The homology of the Brauer algebras ⋮ Symmetric group characters as symmetric functions ⋮ Representation stability for syzygies of line bundles on Segre-Veronese varieties ⋮ Factorization statistics and the twisted Grothendieck-Lefschetz formula ⋮ Coinduction functor in representation stability theory ⋮ Asymptotic growth of Betti numbers of ordered configuration spaces of an elliptic curve ⋮ Categories of dimension zero ⋮ Representation stability in the level 4 braid group ⋮ The equivariant Kazhdan-Lusztig polynomial of a matroid ⋮ Johnson homomorphisms ⋮ Virtual Specht stability for \(FI\)-modules in positive characteristic ⋮ Homological stability for automorphism groups ⋮ On the second homology group of the Torelli subgroup of \(\Aut(F_n)\) ⋮ Asymptotic behavior of representations of graded categories with inductive functors ⋮ Motivic random variables and representation stability. I: Configuration spaces ⋮ Homology of braid groups, the Burau representation, and points on superelliptic curves over finite fields ⋮ STABILITY PATTERNS IN REPRESENTATION THEORY ⋮ Representation theory for the Križ model ⋮ Representation stability for families of linear subspace arrangements ⋮ The symmetric group action on rank-selected posets of injective words ⋮ Generators for the representation rings of certain wreath products ⋮ Representation stability for diagram algebras ⋮ Motivic random variables and representation stability. II: Hypersurface sections ⋮ Partial Torelli groups and homological stability ⋮ Generalized representation stability and 𝐹𝐼_{𝑑}-modules ⋮ Stability in the homology of congruence subgroups. ⋮ Central stability homology ⋮ On the homology of the noncrossing partition lattice and the Milnor fibre ⋮ Categorifications of rational Hilbert series and characters of \(\boldsymbol{FS}^{\mathrm{op}}\) modules ⋮ Some examples of simple generic 𝐹𝐼-modules in positive characteristic ⋮ Regularity and stable ranges of \textbf{FI}-modules ⋮ Representation stability and finite orthogonal groups ⋮ All linear symmetries of the SU(3) tensor multiplicities ⋮ Homological stability for configuration spaces of manifolds ⋮ A representation stability theorem for VI-modules ⋮ Representation stability for the cohomology of the pure string motion groups. ⋮ On the distribution of the major index on standard Young tableaux ⋮ Stable decompositions for some symmetric group characters arising in braid group cohomology. ⋮ Koszulity of directed categories in representation stability theory ⋮ On computing the eventual behavior of an 𝐹𝐼-module over the rational numbers ⋮ The Cohomology of $$\mathcal{M}_{0,n}$$ as an FI-Module ⋮ Homological invariants of \(\mathrm{FI}\)-modules and \(\mathrm{FI}_{G}\)-modules ⋮ Representation stability for homotopy groups of configuration spaces ⋮ Polynomial splitting measures and cohomology of the pure braid group ⋮ Towards representation stability for the second homology of the Torelli group. ⋮ A geometric approach to counting norms in cyclic extensions of function fields ⋮ An inductive method for OI-modules ⋮ \(FI\)-modules over preadditive categories and torsion theories ⋮ Representation stability for the cohomology of the moduli space \(\mathcal M_{g}^{n}\) ⋮ GL-EQUIVARIANT MODULES OVER POLYNOMIAL RINGS IN INFINITELY MANY VARIABLES. II ⋮ FI-modules over Noetherian rings. ⋮ Topology of arrangements and representation stability. Abstracts from the workshop held January 14--20, 2018 ⋮ \(\mathrm{FI}_{\mathcal{W}}\)-modules and constraints on classical Weyl group characters ⋮ On the cohomology of pure mapping class groups as FI-modules ⋮ Local cohomology and the multigraded regularity of \(\mathcal{FI}^m\)-modules ⋮ Homological stability for moduli spaces of disconnected submanifolds. I ⋮ Depth and the local cohomology of \(\mathcal{FI}_G\)-modules ⋮ Simplicial G-complexes and representation stability of polyhedral products ⋮ Kazhdan-Lusztig polynomials of matroids: a survey of results and conjectures ⋮ Diophantine approximation on matrices and Lie groups ⋮ Splitting behavior of \(S_n\)-polynomials ⋮ Representation stability for pure braid group Milnor fibers ⋮ Convergence criteria for \(\text{FI}_{\mathcal{W}}\)-algebras and polynomial statistics on maximal tori in type B/C ⋮ Categories of FI type: a unified approach to generalizing representation stability and character polynomials ⋮ FI-sets with relations ⋮ Stacks and torsors over quivers. ⋮ VI-modules in nondescribing characteristic. I ⋮ Representation stability for filtrations of Torelli groups ⋮ Representation stability for the cohomology of arrangements associated to root systems ⋮ Asymptotic normality of the major index on standard tableaux ⋮ Stable decompositions of certain representations of the finite general linear groups ⋮ Filtrations and homological degrees of FI-modules ⋮ A decomposition of the group algebra of a hyperoctahedral group ⋮ An application of the theory of FI-algebras to graph configuration spaces ⋮ Representation stability of the cohomology of Springer varieties and some combinatorial consequences ⋮ Spaces of commuting elements in the classical groups ⋮ The Hopf structure of symmetric group characters as symmetric functions ⋮ Equivariant group presentations and the second homology group of the Torelli group ⋮ Hilbert series in the category of trees with contractions ⋮ Spectra of Symmetrized Shuffling Operators ⋮ \(\mathrm{FI}_{\mathcal W}\)-modules and stability criteria for representations of classical Weyl groups. ⋮ Gröbner methods for representations of combinatorial categories ⋮ Stability of the Heisenberg product on symmetric functions ⋮ Representation stability on the cohomology of complements of subspace arrangements ⋮ Representation stability for the pure cactus group ⋮ Central stability for the homology of congruence subgroups and the second homology of Torelli groups ⋮ Representation stability and outer automorphism groups ⋮ A combinatorial model for the decomposition of multivariate polynomial rings as \(S_n\)-modules ⋮ \texttt{VIC}-modules over noncommutative rings ⋮ Homological stability of topological moduli spaces ⋮ Configuration spaces of graphs with certain permitted collisions ⋮ Families of nested graphs with compatible symmetric-group actions ⋮ Homological degrees of representations of categories with shift functors ⋮ Equivariant topology of configuration spaces ⋮ FI-modules and stability for representations of symmetric groups ⋮ Twisted homological stability for extensions and automorphism groups of free nilpotent groups ⋮ Homological stability for completed homology ⋮ A spectral sequence for stratified spaces and configuration spaces of points

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Picard group of the moduli space of curves with level structures
• Homological stability for configuration spaces of manifolds
• Representation stability for the cohomology of the pure string motion groups.
• Towards representation stability for the second homology of the Torelli group.
• FI-modules over Noetherian rings.
• On the cohomology of pure mapping class groups as FI-modules
• Stable homology of automorphism groups of free groups.
• Representation stability for the cohomology of the moduli space \(\mathcal M_{g}^{n}\)
• The stability of the Kronecker product of Schur functions
• Density properties for certain subgroups of semi-simple groups without compact components
• Stability in the homology of congruence subgroups.
• Torsion in the Abelianization of the Torelli group \(\mathcal T\) as an \(\mathrm{Sp}(\mathbb Z_2)\)-module.
• The structure of the Torelli group. III: The abelianization of \({\mathcal S}\)
• Série de Poincaré-Koszul associée aux groupes de tresses pures
• On the action of the symmetric group on the cohomology of the complement of its reflecting hyperplanes
• On the eigenvalues of representations of reflection groups and wreath products
• Combinatorics and topology of complements of hyperplanes
• Some aspects of groups acting on finite posets
• Galois representations attached to mod \(p\) cohomology of \(GL(n,\mathbb{Z})\)
• On the cohomology of an arrangement of type \(B_ l\)
• The Torelli groups for genus 2 and 3 surfaces
• Stability of Schur functors
• The cohomology ring of the colored braid group
• The cohomology of the cotangent bundle of Heisenberg groups.
• Automorphisms and cohomology of discrete groups
• Syzygies of Segre embeddings and \(\Delta\)-modules
• FI-modules and stability for representations of symmetric groups
• Stable decompositions for some symmetric group characters arising in braid group cohomology.
• The stable moduli space of Riemann surfaces: Mumford's conjecture
• Dimension of the Torelli group for \(\text{Out}(F_n)\).
• The integral cohomology of the group of loops.
• Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)
• On the descending central series of groups with a single defining relation
• Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts
• On the cohomology of compact homogeneous spaces of nilpotent Lie groups
• GL-equivariant modules over polynomial rings in infinitely many variables
• Completed cohomology – a survey
• STABILITY PATTERNS IN REPRESENTATION THEORY
• The Adjoint Homology of the Free 2-Step Nilpotent Lie Algebra
• Representation Stability of Power Sets and Square Free Polynomials
• Parameterized Abel-Jacobi maps and abelian cycles in the Torelli group
• On the problem of homology stability for congruence subgroups
• Representation stability in cohomology and asymptotics for families of varieties over finite fields
• The Minimal Model of the Complement of an Arrangement of Hyperplanes
• Permutation representations on Schubert varieties
• Stability phenomena in the topology of moduli spaces
• The dimension of the Torelli group
• On the Complete GL(n, C)-Decomposition of the Stable Cohomology of gl n (A)
• Infinitesimal presentations of the Torelli groups
• Braid groups and loop spaces
• Torelli Groups and Geometry of Moduli Spaces of Curves
• On the Steinberg Character of a Finite Simple Group of Lie Type
• On the homology and cohomology of congruence subgroups

This page was built for publication: Representation theory and homological stability.