Related papers: Modular principal series representations

Let $G$ be a finite group of Lie type and $\ell$ be a prime which is not equal to the defining characteristic of $G$. In this note we discuss some open problems concerning the $\ell$-modular irreducible representations of $G$. We also…

For a local field $F$ we consider tamely ramified principal series representations $V$ of $G={\rm GL}_{d+1}(F)$ with coefficients in a finite extension $K$ of ${\mathbb Q}_p$. Let $I_0$ be a pro-$p$-Iwahori subgroup in $G$, let ${\mathcal…

Let $G$ be a connected reductive group defined and split over a non-archimedean local field $F$. We give a new geometric proof of a special case of a recent theorem of Solleveld. Namely, we show that the class of standard Iwahori-spherical…

In this paper, we establish general categorical frameworks that extend Loewy's classification scheme for finite-dimensional real irreducible representations of groups and Borel--Tits' criterion for the existence of rational forms of…

Motivated by the maximal subgroup problem of the finite classical groups we begin the classification of imprimitive irreducible modules of finite quasisimple groups. We obtain our strongest results for modules over fields of characteristic…

We introduce the definition of the typical irreducible modules of the generalized quantum groups, and prove the Weyl-Kac-type formulas of their characters. As a by-product, we obtain the Weyl-Kac-type character formulas of the typical…

Suppose $\ell$ is a prime number, ${\mathbf Q}_\ell$ is the field of $\ell$-adic numbers, ${\mathbf F}_\ell$ is the finite field of $\ell$ elements, and $d$ is a positive integer. Suppose $G$ is a finite subgroup of a symplectic group…

We prove a long-standing conjecture of Geck which predicts that cuspidal unipotent characters remain irreducible after $\ell$-reduction. To this end, we construct a progenerator for the category of representations of a finite reductive…

In this manuscript we make a general study of the representations realized, for a reductive Lie group of Harish-Chandra class, on the compactly supported sheaf cohomology groups of an irreducible finite-rank polarized homogeneous vector…

We introduce a generalized version of a q-Schur algebra (of parabolic type) for arbitrary Hecke algebras over extended Weyl groups. We describe how the decomposition matrix of a finite group with split BN-pair, with respect to a…

We determine precisely the number of irreducible summands of an irreducible cross characteristic representation of $GL_{n}(q)$ on restriction to $SL_{n}(q)$. Combined with a recent result of C. Bonnafe, this yields a canonical labeling for…

In this paper, we begin with the classification of Harish-Chandra imprimitive representations in non-defining characteristic. We recall the connection of this problem to certain generalizations of Iwahori-Hecke algebras and show that…

Let $G_{\mathbb R}$ be the set of real points of a complex linear reductive group and $\hat G_\lambda$ its classes of irreducible admissible representations with infinitesimal integral regular character $\lambda$. In this case each cell of…

We obtain an irreducibility criterion for generalized principal series, extending known and frequently employed results for principal series. Our approach rests on a newly observed semi-direct product decomposition of the relative Weyl…

We classify and explicitly construct the irreducible graded representations of anti-spherical Hecke categories which are concentrated in one degree. Each of these homogeneous representations is one-dimensional and can be cohomologically…

The present paper deals with the representation theory of the reflection equation algebra, connected with a Hecke type R-matrix. Up to some reasonable additional conditions the R-matrix is arbitrary (not necessary originated from quantum…

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…

The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra $\Lambda$ are explored, with regard to both their geometry and the structure of the modules they encode. Provided…

We prove irreducible components of moduli spaces of semistable representations of skewed-gentle algebras, and more generally, clannish algebras, are isomorphic to products of projective spaces. This is achieved by showing irreducible…

The purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie…