Related papers: Representation stability for sequences of 0-Hecke …
In this paper we introduce the notion of the stability of a sequence of modules over Hecke algebras. We prove that a finitely generated consistent sequence associated with Hecke algebras is representation stable.
Representation stability is a theory describing a way in which a sequence of representations of different groups is related, and essentially contains a finite amount of information. Starting with Church-Ellenberg-Farb's theory of…
A VI-module gives rise to a sequence of representations of the finite general linear groups. We prove that the sequence obtained from any finitely generated VI-module over an algebraically closed field of characteristic zero is…
We first consider the rational Cherednik algebra corresponding to the action of a finite group on a complex variety, as defined by Etingof. We define a category of representations of this algebra which is analogous to "category O" for the…
Representation stability is a phenomenon whereby the structure of certain sequences $X_n$ of spaces can be seen to stabilize when viewed through the lens of representation theory. In this paper I describe this phenomenon and sketch a…
A category of FI type is one which is sufficiently similar to finite sets and injections so as to admit nice representation stability results. Several common examples admit a Grothendieck fibration to finite sets and injections. We begin by…
We introduce a functor calculus for functors $\mathsf{FI}\to\mathcal{V}$, which we call $\mathsf{FI}$-objects, for $\mathsf{FI}$ the category of finite sets and injections and $\mathcal{V}$ a stable presentable $\infty$-category. We show…
These notes are based on a course given at the EPFL in May 2005. It is concerned with the representation theory of Hecke algebras in the non-semisimple case. We explain the role that these algebras play in the modular representation theory…
For a noetherian scheme, we introduce its unbounded stable derived category. This leads to a recollement which reflects the passage from the bounded derived category of coherent sheaves to the quotient modulo the subcategory of perfect…
In this survey article we summarize the current state of research in representation stability theory. We look at three different, yet related, approaches, using (1) the category of FI-modules, (2) Schur-Weyl duality, and (3)…
We construct a family of exact functors from the BGG category of representations of the Lie algebra sl to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra H of GL. These functors…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
In this paper we introduce and develop the theory of FI-modules. We apply this theory to obtain new theorems about: - the cohomology of the configuration space of n distinct ordered points on an arbitrary (connected, oriented) manifold -…
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…
Jensen, Su, and Yang described the projective indecomposable modules of the $0$-Schur algebra $\mathbf{S}_0(n,r)$ using its geometric realization. In this paper, the simple modules of $\mathbf{S}_0(n,r)$ are identified by computing the tops…
We study the representation theory of the infinite type A Hecke algebra over a non-archimedean field in the case where the parameter is a pseudo-uniformizer. Specifically, we consider a family of representations, called almost-symmetric,…
Persistence modules are representations of products of totally ordered sets in the category of vector spaces. They appear naturally in the representation theory of algebras, but in recent years they have also found applications in other…
In this paper we give a new proof for the classification of irreducible modules of an affine Hecke algebra of type $A_n$, which was obtained by G. E. Murphy in 1995.
Let $F$ be a local field of mixed characteristic, let $k$ be a finite extension of its residue field, let ${\mathcal H}$ be the pro-$p$-Iwahori Hecke $k$-algebra attached to ${\rm GL}_{d+1}(F)$ for some $d\ge1$. We construct an exact and…
We study asymptotic properties of the modular representation theory of symmetric groups and investigate modular analogs of stabilization phenomena in characteristic zero. The main results are equivalences of categories between certain…