Related papers: A comparison between pro-$p$ Iwahori-Hecke modules…

We introduce the notion of a dilation for a partial representation (i.e. a partial module) of a Hopf algebra, which in case the partial representation origins from a partial action (i.e.a partial module algebra) coincides with the…

In this paper we establish a connection between the cohomology of a modular Lie algebra and its p-envelopes. We also compute the cohomology of Zassenhaus algebras and their minimal p-envelopes with coefficients in generalized baby Verma…

Hopf representation is a module and comodule with a consistency condition that is more general than the consistency condition of Hopf modules. For a Hopf algebra $H$, we construct an induced Hopf representation from a representation of a…

In a letter to Tate, Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions on an adelic double coset space constructed from the endomorphism algebra of…

I withdraw this article because one of the references has changed in the meantime.

Let $G/H$ be a Galois symmetric space for an unramified quadratic extension of a locally compact field $F$, where the group $H$ is semisimple, simply connected, defined and split over $F$. We prove that there exists a subgroup $\Gamma =…

Let $\mathfrak F$ be a locally compact nonarchimedean field with residue characteristic $p$ and $G$ the group of $\mathfrak{F}$-rational points of a connected split reductive group over $\mathfrak{F}$. We define a torsion pair in the…

We develop some techniques to the study of exact module categories over some families of pointed finite-dimensional Hopf algebras. As an application we classify exact module categories over the tensor category of representations of the…

Let G be a split reductive group over the integers, F a p-adic local field with residue field Fq. We relate the pro-p-Iwahori Hecke algebra H of G(F) over Fq to the Vinberg monoid of the dual group and study this relation. As an…

We prove a reciprocity law for one-dimensional compatible systems of mod p representations of absolute Galois groups of number fields. We prove that these arise from Hecke characters, and in particular recover by purely algebraic means the…

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…

Hilbert space representations of the cross product *-algebra of the Hopf *-algebra U_q(su_2) and its module *-algebras O(S^2_{qc}) of Podles' spheres are studied. Two classes of representations are described by explicit formulas for the…

Let $G$ be a direct product of inner forms of general linear groups over non-archimedean locally compact fields of residue characteristic $p$ and let $K^1$ be the pro-$p$-radical of a maximal compact open subgroup of $G$. In this paper we…

We show that, under suitable assumptions, the systems of Hecke eigenvalues arising from (mod p) modular forms of PEL-type associated to an algebraic group G of type A or C coincide with the Hecke eigensystems arising from (mod p) algebraic…

We establish a lower bound for the representation dimension of all the classical Hecke algebras of types A, B and D. For all the type A algebras, and most of the algebras of types B and D, we also establish upper bounds. Moreover, we…

We give a classification of irreducible admissible modulo $p$ representations of a split $p$-adic reductive group in terms of supersingular representations. This is a generalization of a theorem of Herzig.

We construct classes of von Neumann algebra modules by considering ``column sums" of noncommutative L^p spaces. Our abstract characterization is based on an L^{p/2}-valued inner product, thereby generalizing Hilbert C*-modules and…

Ideas from Hodge theory have found important applications in representation theory. We give a survey of joint work with Ben Elias which uncovers Hodge theoretic structure in the Hecke category ("Soergel bimodules"). We also outline…

Following Gluck and Wolf we complete the It\^o--Michler's Theorem for the projective representations of a $p$-solvable or $\pi$-separable group, and then we relate the projective irreducible modules of such a group with those of its Sylow…

We suggest a simple definition for categorification of modules over rings and illustrate it by categorifying integral Specht modules over the symmetric group and its Hecke algebra via the action of translation functors on some subcategories…