Related papers: Quantitative representation stability over linear …
In this paper we consider some classical varieties of linear algebras over the field which has characteristic 0. For every considered variety we take a category of the finite generated free algebras of this variety. And for every this…
We define a notion of virtual Specht stability which is a relaxation of the Church-Farb notion of representation stability for sequences of symmetric group representations. Using a structural result of Nagpal, we show that $FI$-modules over…
We prove an explicit and sharp upper bound for the Castelnuovo-Mumford regularity of an FI-module V in terms of the degrees of its generators and relations. We use this to refine a result of Putman on the stability of homology of congruence…
The groups $\Gamma_{n,s}$ are defined in terms of homotopy equivalences of certain graphs, and are natural generalisations of $\mbox{Out}(F_n)$ and $\mbox{Aut}(F_n)$. They have appeared frequently in the study of free group automorphisms,…
This paper is a short account of the construction of a new class of the infinite-dimensional representations of the quantum groups. The examples include finite-dimensional quantum groups $U_q(\mathfrak{g})$, Yangian $Y(\mathfrak{g})$ and…
Using a result of Gan and Li on FI-hyperhomology and a semi-simplicial resolution of configuration spaces due to Randal-Williams, we establish an improved representation stability stable range for configuration spaces of distinct ordered…
The main result of this paper is an application of the topology of the space $Q(X)$ to obtain results for the cohomology of the symmetric group on $d$ letters, $\Sigma_d$, with `twisted' coefficients in various choices of Young modules and…
We study representation stability in the sense of Church, Ellenberg, and Farb \cite{FI-module} through the lens of symmetric function theory and the different symmetric function bases. We show that a sequence, $(F_n)_n$, where $F_n$ is a…
A discrete countable group G is matricially stable if the finite dimensional approximate unitary representations of G are perturbable to genuine representations in the point-norm topology. For large classes of groups G, we show that…
In this paper we use the quantization of fields based on Geometric Langlands Correspondence \cite{diep1} to realize the automorphic representations of some concrete series of groups: for the affine Heisenberg (loop) groups it is reduced to…
We study the coinduction functor on the category of FI-modules and its variants. Using the coinduction functor, we give new and simpler proofs of (generalizations of) various results on homological properties of FI-modules. We also prove…
Homological stability has shown itself to be a powerful tool for the computation of homology of families of groups such as general linear groups, mapping class groups or automorphisms of free groups. We survey here tools and techniques for…
We say a representation V of a group G has stability if its multiplicities m^{G}_{V}(\lambda) is dependent only on some equivalence class of \lambda for a sufficiently large parameter \lambda. In this paper, we prove that the restriction of…
Let $k$ be a commutative Noetherian ring and $\underline{\mathscr{C}}$ be a locally finite $k$-linear category equipped with a self-embedding functor of degree 1. We show under a moderate condition that finitely generated torsion…
We introduce the notion of a neutral representation of a finite group, or finite group scheme, $G$; a representation $V$ with the property that if a gerbe $\mathcal{G}$ over a field $k$ that is a form of the classifying stack $\mathcal{B}…
We study uniform stability of discrete groups, Lie groups and Lie algebras in the rank metric, and the connections between uniform stability of these objects. We prove that semisimple Lie algebras are far from being flexibly…
The fundamental group of the real locus of the Deligne-Mumford compactification of the moduli space of rational curves with $n$ marked points, the pure cactus group, resembles the pure braid group in many ways. As it is the case for several…
We introduce a strong notion of quasiconvexity in finitely generated groups, which we call stability. Stability agrees with quasiconvexity in hyperbolic groups and is preserved under quasi-isometry for finitely generated groups. We show…
We study $\epsilon$-representations of discrete groups by unitary operators on a Hilbert space. We define the notion of Ulam stability of a group which loosely means that finite-dimensional $\epsilon$-represendations are uniformly close to…
We introduce FI-algebras over a commutative ring $K$ and the category of FI-modules over an FI-algebra. Such a module may be considered as a family of invariant modules over compatible varying $K$-algebras. FI-modules over $K$ correspond to…