Related papers: From pro-$p$ Iwahori-Hecke modules to $(\varphi,\G…

In this article we study the representations of general linear groups which arise from their action on flag spaces. These representations can be decomposed into irreducibles by proving that the associated Hecke algebra is cellular. We give…

Let X be the group of weights of a maximal torus of a simply connected semisimple group over C and let W be the Weyl group. The semidirect product W(Q\otimes X/X) is called the extended Weyl group. There is a natural C(v)-algebra H called…

In the first part of this paper we present explicit formulas for primitive idempotents in arbitrary Frobenius algebras using the entries of representing matrices coming from projective indecomposable modules with respect to a certain choice…

We calculate the extension groups between simple modules of pro-$p$-Iwahori Hecke algebras.

Let $\Delta$ be a closed, cocompact subgroup of $G \times \widehat{G}$, where $G$ is a second countable, locally compact abelian group. Using localization of Hilbert $C^*$-modules, we show that the Heisenberg module…

We define and study stacks which parametrize Lubin--Tate $(\varphi,\Gamma)$-modules. By working at a perfectoid level, we compare these with the Emerton--Gee stacks of cyclotomic $(\varphi,\Gamma)$-modules. As a consequence, we deduce…

We consider the problem of classifying irreducible Specht modules for the Iwahori-Hecke algebra of type B with parameters Q,q. We solve this problem completely in the case where q is not a root of unity, and in the case q=-1 we reduce the…

This note is an appendix to a preprint by E. Hellmann. We give a complete classification of simple objects of the category of vector spaces D over K = Fpbar((u)) equipped with an endomorphism phi whose image generates D and that are…

Let $R$ be a ring and $\mathsf S$ be a class of strongly finitely presented (FP${}_\infty$) $R$-modules closed under extensions, direct summands, and syzygies. Let $(\mathsf A,\mathsf B)$ be the (hereditary complete) cotorsion pair…

Let $(R, \mf, k_R)$ be regular local $k$-algebra satisfying the weak Jacobian criterion, such that $k_R/k$ is an algebraic field extension. Let $D_R$ be the ring of $k$-linear differential operators of $R$. We give an explicit decomposition…

We derive a parameterization of simple modules for the cyclotomic Hecke algebras of type $G(r,p,n)$ over field of any (coprime to $p$) characteristic. We give explicit formulas for the number of simple modules over these cyclotomic Hecke…

Let $k$ be an algebraically closed field of characteristic $p\ge 0$. Let $G$ be an affine group scheme over $k$. We classify the indecomposable exact module categories over the rigid tensor category $\text{Coh}_f(G)$ of coherent sheaves of…

Let $G$ be a split reductive group over a finite field $k$. In this note we study the space $V$ of finitely supported functions on the set of isomorphism classes $G$-bundles on the projective line ${\mathbb P}^1$ endowed with a…

Let $o$ be the ring of integers in a finite extension $K/\mathbb{Q}_p$ and $G=\mathbf{G}(\mathbb{Q}_p)$ be the $\mathbb{Q}_p$-points of a $\mathbb{Q}_p$-split reductive group $\mathbf{G}$ defined over $\mathbb{Z}_p$ with connected centre…

We associate with every Renner monoid $R$ a \emph{generic Hecke algebra} $\H(R)$ over $\mathbb{Z}[q]$ which is a deformation of the monoid $\mathbb{Z}$-algebra of $R$. If $M$ is a finite reductive monoid with Borel subgroup $B$ and…

Let $\mathrm{VI}$ be the category of finite dimensional $\mathbb{F}_q$-vector spaces whose morphisms are injective linear maps, and let $\mathbf{k}$ be a noetherian ring. We study the category of functors from $\mathrm{VI}$ to…

Let $G$ be a finite group and let $F$ be a finite field of characteristic $2$. We introduce \emph{$F$-special subgroups} and \emph{$F$-special elements} of $G$. In the case where $F$ contains a $p$th primitive root of unity for each odd…

Let $G$ be a finite group and $H$ a normal subgroup of prime index $p$. Let $V$ be an irreducible ${\mathbb F}H$-module and $U$ a quotient of the induced ${\mathbb F}G$-module $V\kern-3pt\uparrow$. We describe the structure of $U$, which is…

Recently, there has been considerable progress in classifying the irreducible representations of Iwahori--Hecke algebras at roots of unity. Here, we present an application of these results to $\ell$-modular Harish--Chandra series for a…

Let $A$ be a commutative noetherian ring, $\frak a$ be an ideal of $A$, $m,n$ be non-negative integers and let $M$ be an $A$-module such that $\Ext^i_A(A/\frak a,M)$ is finitely generated for all $i\leq m+n$. We define a class $\cS_n(\frak…