Restriction of a cuspidal module for finite general linear groups

On the U−module Structure of Unipotent Specht Modules of Finite General Linear Groups

On Cuspidal Representations of General Linear Groups over Discrete Valuation Rings

We define a new notion of cuspidality for representations of GLn over a finite quotient ok of the ring of integers o of a non-Archimedean local field F using geometric and infinitesimal induction functors, which involve automorphism groups Gλ of torsion o-modules. When n is a prime, we show that this notion of cuspidality is equivalent to strong cuspidality, which arises in the construction of ...

On Cuspidal Representations of General Linear Groups over Dicrete Valuation Rings

We define a new notion of cuspidality for representations of GLn over a finite quotient ok of the ring of integers o of a non-Archimedean local field F using geometric and infinitesimal induction functors, which involve automorphism groups Gλ of torsion o-modules. When n is a prime, we show that this notion of cuspidality is equivalent to strong cuspidality, which arises in the construction of ...

On Crdaha and Finite General Linear and Unitary Groups

We show a connection between Lusztig induction operators in finite general linear and unitary groups and parabolic induction in cyclotomic rational double affine Hecke algebras. Two applications are given: an explanation of a bijection result of Broué, Malle and Michel, and some results on modular decomposition numbers of finite general groups. 2010 AMS Subject Classification: 20C33 Dedicated t...

Radon Transforms and the Finite General Linear Groups

Using a class sum and a collection of related Radon transforms, we present a proof G. James’s Kernel Intersection Theorem for the complex unipotent representations of the finite general linear groups. The approach is analogous to that used by F. Scarabotti for a proof of James’s Kernel Intersection Theorem for the symmetric group. In the process, we also show that a single class sum may be used...