Categories of FI type: a unified approach to generalizing representation stability and character polynomials

DOI10.1016/j.jalgebra.2017.03.010zbMath1391.20010arXiv1608.02664OpenAlexW2519744292MaRDI QIDQ524494

Nir Gadish

Publication date: 2 May 2017

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

Full work available at URL: https://arxiv.org/abs/1608.02664

zbMATH Keywords

representations of symmetric groupsrepresentation stabilityFI-modulescharacter polynomials

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Cohomology of groups (20J06) Module categories and commutative rings (13C60)

Related Items

Asymptotic behaviors in the homology of symmetric group and finite general linear group quandles, Castelnuovo-Mumford regularity of representations of certain product categories, Asymptotic behavior of representations of graded categories with inductive functors, Representation stability for families of linear subspace arrangements, Product expansions of \(q\)-character polynomials, Some examples of simple generic 𝐹𝐼-modules in positive characteristic, A classification of injective FI ^m -modules, An inductive machinery for representations of categories with shift functors, Topology of arrangements and representation stability. Abstracts from the workshop held January 14--20, 2018, \(\mathrm{FI}^{m}\)-modules over Noetherian rings, Local cohomology and the multigraded regularity of \(\mathcal{FI}^m\)-modules, VI-modules in nondescribing characteristic. I, Dimension-independent statistics of 𝐺𝑙_{𝑛}(𝔽_{𝕢}) via character polynomials, Families of nested graphs with compatible symmetric-group actions

Cites Work

• Unnamed Item
• Homological stability for configuration spaces of manifolds
• \(\mathrm{FI}_{\mathcal W}\)-modules and stability criteria for representations of classical Weyl groups.
• Transformation groups
• Representation stability for families of linear subspace arrangements
• Configuration spaces of algebraic varieties
• Noetherian property of infinite EI categories
• FI-modules and stability for representations of symmetric groups
• Representation theory and homological stability.
• GL-equivariant modules over polynomial rings in infinitely many variables
• Representation stability in cohomology and asymptotics for families of varieties over finite fields
• Coinduction functor in representation stability theory
• Representation Stability